Both players score in 1-0 victories over Valladolid and Rayo Vallecano, respectively, as Real Madrid play on Sunday night
Dembele and Griezmann score as Barcelona and Atletico Madrid eke out wins
Ousmane Dembele's second-half strike was the difference as reigning Primera Liga champions Barcelona ground out a 1-0 win away to newly-promoted Valladolid on Saturday to maintain their perfect start to the campaign.
It was not a classic Barcelona performance by any means at the Estadio Jose Zorrilla, and they escaped at the death as a Keko equaliser for the hosts was disallowed due to a marginal offside call.
Nevertheless, Ernesto Valverde's side now have six points out of six and are yet to concede a goal, with this victory following a 3-0 success against Alaves on the opening weekend.
Lionel Messi had scored twice in that game, but he struggled to make an impact here on a dreadful pitch that kept cutting up.
Instead it was Philippe Coutinho who came closest to opening the scoring in the first half, his low shot from the edge of the area heading for the corner before Jordi Masip turned it around the post.
On a night when Gerard Pique made his 300th appearance in the Primera Liga, none of Barcelona's close-season signings started, although Arturo Vidal and Brazilian winger Malcom came off the bench late on.
By that time Dembele, whose first season at Barca after joining from Borussia Dortmund was marred by injury, had scored the crucial goal. Sergi Roberto headed a 57th-minute cross back down into the path of the French international, who swept the ball past Masip.
The visitors then thought they had scored a second in the closing stages as Messi released Luis Suarez to slot home, but the offside flag cut short the celebrations.
Barca were then rescued by the Video Assistant Referee in the second minute of added time. Substitute Keko, having earlier headed a glorious chance straight at Marc-Andre ter Stegen, this time saw his header find the back of the net.
The Valladolid fans, who saw their team win promotion via the play-offs, erupted in celebration, but the assistant referee had spotted the offside, and video replays confirmed it was the right decision, if only just.
'Growing in strength'
Barcelona's win followed a similarly unspectacular victory for Atletico Madrid earlier, as the Europa League holders beat Rayo Vallecano 1-0 in a capital derby.
Antoine Griezmann, a member of France's World Cup-winning squad along with Dembele, scored the only goal of the game in the 63rd minute at the Wanda Metropolitano as Diego Simeone's men notched their first league win of the campaign.
Atletico, tipped to challenge Barcelona and Real Madrid for the title this term, kicked off their campaign with a 1-1 draw at Valencia last weekend.
Despite labouring for long periods, they proved too strong for an impressive Rayo, who were champions of the second-tier last term but have lost both games so far this season.
"It was a difficult match from the start and Rayo played well, but we feel good because we won, and because it's not easy at the start of the season and everyone is struggling," Simeone said.
"Griezmann is growing in strength. We are trying to get him up to his best form with the more minutes he plays."
The goal came when Montenegrin centre-back Stefan Savic climbed highest to nod down a corner, and Griezmann, who scored 29 times in all competitions last season, swivelled to slot into the net.
Atletico struggled to close out the win, though, with goalkeeper Jan Oblak having to keep out Adri Embarba's free-kick and dive at the feet of Alex Moreno to smother the full-back's effort.
But the Slovenian 'keeper kept his best save for the 90th minute, as he sprung to his right to beat away Sergio Moreno's well-struck shot and ensure Atletico took all three points.
Earlier on Saturday, Alaves and Real Betis played out a goalless draw as both teams got off the mark for the season after defeats last week.
After beating Getafe 2-0 last weekend, Real Madrid go to Girona on Sunday night.