Barcelona maintained their 100% record in the Primera Liga with a 1-0 win over Valencia, while Bayern Munich crushed Stuttgart 6-1 to move to the top of the Bundesliga.
European round-up: Ibrahimovich inspires first PSG win as Juventus hammer Udinese
Barcelona retained the only 100% record in the Primera Liga after a fine strike by Adriano sunk struggling Valencia 1-0.
Tito Vilanova's side could have won by a greater margin had Cesc Fabregas not failed to take two good chances - and were almost made to pay after Valencia's Roberto Soldado and Victor Ruiz both went close - the latter also having a goal disallowed for offside.
Real Madrid registered their first league victory of the season after a comfortable 3-0 win over Granada at the Bernabeu.
Cristiano Ronaldo bagged a brace, and substitute Gonzalo Higuain was also on target as Jose Mourinho's side ensured there was no hangover from their Supercopa success.
The visitors ended the game with 10 men after Borja Gomez was sent off for two yellow cards.
Levante netted a stoppage-time winner to cap a stunning comeback against Espanyol and earn their first Primera Division win of the campaign.
Espanyol had looked on course to claim their own maiden victory after establishing a 2-0 lead inside the opening 25 minutes through fine efforts from summer signings Samuele Longo and Sergio Tejera.
However, Levante hit back at the start of the second half to draw level with quick-fire goals from Juanlu and Christian Lell and then, despite losing striker Vicente Iborra to an 82nd-minute red card, the home side snatched the points when Michel's cross was deflected in three minutes into stoppage time to cap a 3-2 win.
Athletic Bilbao put an end to their nightmare start to the season with a comfortable 2-0 win over Real Valladolid at San Mames.
Marcelo Bielsa's men had conceded nine goals in losing their first two games of the campaign, but put in a far more composed display and were rewarded 20 minutes from time when Aritz Aduriz stroked home his first league goal since returning to the club.
Markel Susaeta then sealed the points five minutes later when he curled beautifully into the top corner.
Sevilla missed two penalties as 10-man Rayo Vallecano clung on for a goalless draw to extend an unbeaten start to the Primera Division season.
Alvaro Negredo was first to miss from the spot on seven minutes after Jordi Amat had pulled down the Spanish international inside the area, but he struck the post and the ball rebounded to safety.
But the visitors were handed another opportunity 20 minutes from time when Ivan Rakitic was brought down by Ruben Martinez.
The goalkeeper was shown a red card but his replacement Dani Gimenez did not even have to make a save as Rakitic pulled his penalty wide.
Serie A champions Juventus sent out a resounding message to their title rivals with a comprehensive 4-1 win over Udinese.
The Old Lady were aided by the 14th-minute dismissal of goalkeeper Zeljko Brkic and Arturo Vidal scored from the resulting penalty, with Mirko Vucinic making it 2-0 on the stroke of half-time.
It was game over eight minutes after the break thanks to Sebastian Giovinco and the same player made it four before Andrea Lazzari grabbed a consolation for the Bianconeri.
Roma also made their intentions for the season clear with an impressive 3-1 win at Inter Milan.
Alessandro Florenzi gave Roma the lead in the 15th minute before a deflected shot from Antonio Cassano brought Inter level in first-half stoppage time.
Daniel Osvaldo restored Roma's lead midway through the second half and Marquinho added a sumptuous winner 10 minutes from time.
The only sour note for Roma came in stoppage time when Osvaldo received a second yellow card.
Lazio maintained their 100% record thanks to their comfortable 3-0 win over Palermo.
The Roman club were grateful to the predatory instincts of Germany striker Miroslav Klose, who book ended a win which also included a strike from Antonio Candreva.
Napoli are also among that group following a 2-1 victory over Fiorentina.
A Borja Valero own goal and Blerim Dzemaili put the home side in control with Stevan Jovetic's reply coming too late for the Viola.
Sampdoria continue to enjoy life back in the top flight as they beat Siena 2-1.
Daniele Gastaldello scored the winner 23 minutes from time after Maxi Lopez and Simone Vergassola had traded goals.
It was a get-out-of-jail goal for Gastaldello too, as he had earlier given away a penalty which led to Vergassola's equaliser.
Francesco Lodi's late free-kick ensured that Catania beat Genoa 3-2 at the Stadio Angelo Massimino.
Juraj Kucka gave the visitors the lead before a double from Gonzalo Bergessio put Catania in front.
Bosko Jakovic levelled things up once more, but Lodi netted with six minutes left to seal the win.
Parma got their campaign up and running at the second attempt with a 2-0 victory over Chievo.
Having lost to Juventus last weekend, Parma had a much easier time of things at the Ennio Tardini Stadium thanks to goals from Ishak Belfodi and Aleandro Rosi.
Cagliari and Atalanta shared the points in a dramatic 1-1 draw.
The visitors overcame the first-half dismissal of Federico Peluso to take the lead through German Denis nine minutes from time.
However, substitute Albin Ekdal snatched a point for Cagliari in the final minute.
Zlatan Ibrahimovic grabbed a brace to inspire Paris St Germain to their first league win of the season at Lille.
Despite their big spending the capital club had only managed to draw their opening three Ligue 1 matches - including goalless encounters in their previous two.
Ibrahimovic, a EU20m (Dh92.3m) summer buy, ensured there was no repeat as he latched onto Maxwell's through ball to score inside 30 seconds - and before Lille had even touched the ball.
Aurelien Chedjou equalised from a corner on 11 minutes before Ibrahimovic, who has scored all his side's league goals this season, won the match when he poked home ahead of Mickael Landreau just before the half-hour.
Marseille top Ligue 1 table following a comfortable victory 3-1 over Rennes.
Jeremy Morel gave the home side a first-half lead and, although Julien Feret levelled for the visitors early in the second, Andre-Pierre-Gignac and a late own goal from Romain Danze secured the points.
The win ensures Ilie Baup's side maintained their 100% start to the season and move two points clear of Lyon.
A last-gasp goal from Mahamane Traore restricted 10-man Bordeaux to a solitary point as Nice claimed a creditable 1-1 draw.
Bayern Munich crushed Stuttgart 6-1 to move ominously to the top of the Bundesliga on a day when the league's most expensive arrival made his debut.
Javi Martinez only played the last 13 minutes, by which time Bayern had already secured the three points with goals from Thomas Muller (two), Toni Kroos, Bastian Schweinsteiger, Luiz Gustavo and Mario Mandzukic.
Vedad Ibisevic was shown a red card on a torrid afternoon for Stuttgart, who took the lead through Martin Harnik.
Szabolcs Huszti inspired Hannover to a resounding 4-0 win over Wolfsburg in a Lower Saxony derby at the VW-Arena.
Newly promoted Dundee lifted themselves off the foot of the SPL with a second minute penalty against Hearts at Tynecastle.
Marian Zaliukas was adjudged to have fouled Colin Nish, and Ryan Conroy stepped up to slot home from the spot.
John Sutton was felled soon afterwards, but saw his penalty to equalise saved by veteran Dee keeper Rab Douglas.
Meanwhile Motherwell moved to the top of the Premier League with a comprehensive 4-1 win over struggling Inverness Caledonian Thistle.
Tom Hateley started the scoring for 'Well in the 11th minute, before Michael Higdon grabbed the first of hat-trick a minute later.
Richie Foran pulled one back on the half-hour mark, but a quick-fire double from Higdon towards the end of the second half put Stuart McCall's side top.
Deadline day signing David Templeton scored a brace for Rangers in Division 3 to as they came back from an early goal to defeat Elgin 5-1.
Benfica top the Liga table on goal difference from Porto thanks to a 3-0 win over Nacional.
Jorge Jesus`s men had to wait until a 51st minute strike from Oscar Cardoza for the breakthrough, before Rodrigo and a second from Cardoza wrapped things up.
Pacos Ferreira also enjoyed a routine win as they saw off Champions League-bound Braga 2-0.
Javier Cohene opened the scoring (13) and Christopher Hurtado made sure of the win 10 minutes from the end.
Beira Mar shared the points with Moreirense, drawing 1-1 at the Estadio Municipal.
Ricardo Pessoa gave the visitors a first-half lead from the spot, but half-time substitute Saleh Javier Al-Shehri ensured Beira hit back.
Elsewhere tonight, Gil Vicente and Vitoria Setúbal drew 0-0, as did Rio Ave and Academica.
Leroy Fer's last-gasp penalty against VVV ensured FC Twente continued their perfect start to the new Eredivisie season.
Second-placed Vitesse Arnhem also had to wait until very late to grab a 1-0 win at home to Feyenoord.
Wilfried Bony scored the goal in injury-time to maintain Vitesse's unbeaten start and leave them two points behind the leaders.
PSV Eindhoven are a point further back after captain Marc van Bommel netted his first goal since returning to the club in a 5-1 thumping of 10-man AZ Alkmaar.
AZ's hopes were immediately undermined by Etienne Reijnen's eight-minute red card although Adam Maher's 28th-minute goal cancelled out Tim Matavz's opener to have them level at half-time.
Van Bommel opened the floodgates after the break though, netting on 54 minutes, before Marcelo (68), Matavz (83) and Atiba Hutchinson (90) made it a rout.
Champions Ajax drew 2-2 at Heerenveen after their South Africa forward Thulani Serero went from hero to villain.
Serero (13, 47) had struck twice either side of goals from Heerenveen's Alfred Finnbogason (30, 45) before he was sent off on 53 minutes.
Despite his dismissal Ajax held on to at least stay unbeaten and behind PSV only on goal difference.