Mourinho sent to the stands as Lukaku's strike earns Manchester United three points at Southampton
Premier League round-up: Philippe Coutinho free kick and Simon Mignolet's penalty save help earn Liverpool three points
Leicester City v Liverpool
Leicester: Okazaki (45+3'), Vardy (69')
Liverpool: Salah (15'), Coutinho (23'), Henderson (68')
Leicester City were left to rue a missed Jamie Vardy penalty for potentially denying them at least a point against Liverpool in Saturday’s late game.
The England striker saw his 70th-minute spot kick saved by Simon Mignolet just minutes after his header had cut Liverpool’s lead.
Mohamad Salah had given Liverpool an early lead as the Egyptian headed in from a tight angle following a Philippe Coutinho cross.
Coutinho doubled the lead eight minutes later as the gifted Brazilian curled home a sumptuous free kick from 25 yards out.
Shinji Okazaki had an effort ruled out for offside for the hosts just before the break but the Japanese striker was on hand to prod home minutes later as Liverpool's familiar failings of dealing with corners once again reared its ugly head.
Jordan Henderson's strike on 68 minutes restored Liverpool's two-goal cushion before Vardy headed into an empty goal a minute later after Mignolet could only parry Demarai Gray's stinging volley.
Mignolet then went from zero to hero in the space of 60 seconds. The Belgian was judged to have fouled Vardy as the striker chased a ball into the box but the goalkeeper saved the same player's well-struck spot kick to redeem himself and earn his team three precious points.
Stoke City 0-4 Chelsea
Chelsea: Morata (2', 77', 82'), Pedro (30')
Chelsea continued to show there is life after Diego Costa with another Premier League victory at Stoke City, with Alvaro Morata scoring a hat-trick in a 4-0 win.
Morata, the club-record signing bought to replace Costa, was on the scoresheet again early on before Pedro extended the lead on the half-hour mark.
Both goals came from defensive mistakes by Stoke, whose manager Mark Hughes had demanded a response from his players following the disappointing midweek defeat at Bristol City in the League Cup. He did not get it, with Morata rounding off the win in the final quarter-hour.
Burnley 0-0 Huddersfield Town
Burnley were held to a goalless draw at home to promoted Huddersfield Town on Saturday in a Premier League game which offered little entertainment.
Burnley striker Chris Wood went close with a header from a Stephen Ward cross in the 23rd minute but that was the only real effort on goal in the opening 45 minutes.
Huddersfield created a chance just after the interval when Tom Ince burst from midfield and set up Laurent Depoitre but the Belgian's low shot was well dealt with by Burnley keeper Nick Pope.
Ince fired wide from 20 metres out after a swift counter-attack and then substitute Rajiv van La Parra was booked for a blatant dive in the penalty area.
Everton 2-1 Bournemouth
Everton: Niasse (77', 82')
Bournemouth: (King 49')
Oumar Niasse came in from the cold to lift Everton as the Senegal forward's second-half double clinched a 2-1 win over Bournemouth on Saturday.
Ronald Koeman's side were heading for a fourth successive Premier League defeat when Josh King put Bournemouth ahead after the interval at Goodison Park.
But Niasse, frozen out for much of last season by Koeman, came off the bench to score twice in his first appearance for Everton in the Premier League since May 2016.
Thanks to Niasse's heroics, Everton won for the first time in five league games to climb out of the relegation zone.
Bournemouth remain in the bottom three after their fifth defeat from six league games.
Manchester City 5-0 Crystal Palace
Man City: Sane (44'), Sterling (51', 59'), Aguero (79'), Delph (89')
Sergio Aguero moved within a goal of Manchester City's all-time record as Pep Guardiola's men thrashed bottom side Crystal Palace 5-0.
Aguero headed a Leroy Sane cross through the grasp of Wayne Hennessey for his 176th goal in City colours during the second half of another commanding display at the Etihad Stadium.
The prolific Argentine now needs just one more goal to equal the record tally of Eric Brook, which has stood since 1939.
Leaders City were already well on the way to victory when Aguero struck their fourth in the 79th minute after an opener from Sane and quickfire double from Raheem Sterling. Substitute Fabian Delph added a superb late fifth.
For Palace the misery continues, although they showed signs of looking more organised under the guidance of former England manager Roy Hodgson.
The Londoners have failed to win in six games without scoring - the longest wait for a first goal of the season in top-flight history.
Southampton 0-1 Manchester United
Man United: Lukaku (20')
Manchester United equalled their best start to a Premier League campaign after Romelu Lukaku scored his eighth goal of the season in all competitions to give them a 1-0 win at Southampton on Saturday.
The result left United second on 16 points from five games, behind leaders Manchester City on goal difference as United's prolific summer signing became the first Premier League player to score for three different clubs against Southampton at their St Mary's Stadium, having also done so with Everton and West Bromwich Albion.
Lukaku scrambled a 20th-minute winner, pouncing on his own rebound in the six-yard box after the home team's keeper Fraser Forster had parried the striker's close-range header following a superb cross from the left by Ashley Young.
United had manager Jose Mourinho sent off in the last minute of stoppage time for dissent as Southampton piled the pressure in the closing stages
Swansea City 1-2 Watford
Swansea: Abraham (56')
Watford: Gray (13'), Richarlison (90)
Richarlison struck a late winner as Watford's 2-1 victory gave them a first league success at Swansea City since 1983.
Luther Blissett and John Barnes were the scorers when Watford last won on Swansea soil.
But Andre Gray and the Brazilian Richarlison were the Watford heroes this time after substitute Tammy Abraham appeared to have given Swansea a share of the spoils.
Abraham finished from close range after 56 minutes to cancel out Gray's first Watford goal, but Richarlison brushed aside Alfie Mawson's timid challenge in the final minute to finish off the underside of the crossbar.
West Ham United 2-3 Tottenham Hotspur
West Ham: Hernandez (65), Kouyate (87')
Spurs: Kane (34', 38'), Eriksen (60)
Red card: Serge Aurier (Spurs)
Tottenham Hotspur secured a 3-2 victory at West Ham United on Saturday, having survived a late comeback from their London rivals and played the last 20 minutes with 10 men.
The result never appeared in doubt as Spurs dominated early on and the pressure told as Harry Kane headed the visitors into a 34th-minute lead, before making it seven goals in six games against West Ham four minutes later.
Christian Eriksen expertly converted from the edge of the box to make it 3-0 on the hour mark, before West Ham's Javier Hernandez tapped home five minutes later to give the home fans hope.
Serge Aurier was then dismissed for a second booking, before Cheikhou Kouyate ensured a nervy finish for Spurs after netting with three minutes to go.
Spurs held on, however, for a fifth successive away win - equalling a club record for victories on the road - a success that piles the pressure on West Ham manager Slaven Bilic.
Brighton & Hove Albion v Newcastle United, 7pm
Arsenal v West Bromwich Albion, 11pm