Madrid see off Mallorca to stay on title course
The France midfielder, who is suspended for the second leg of Madrid's Champions League quarter-final away to Manchester City next week, scored three minutes into the second half with a deflected 25-metre drive.
Jude Bellingham rattled the crossbar in the first half with a rasping effort from just outside the area as coach Carlo Ancelotti reshuffled his attack with Wednesday's trip to England in mind, leaving out Vinicius Junior and Rodrygo.
Tchouameni's third goal of the season put Madrid ahead, with Brahim Diaz denied a second by the legs of Mallorca goalkeeper Predrag Rajkovic and Fede Valverde's attempt cleared off the line.
Vinicius appeared off the bench for the last 30 minutes but Rodrygo and Toni Kroos were unused substitutes after a thrilling 3-3 draw with City in Tuesday's first leg.
Sergi Darder's spectacular dipping shot forced a flying stop from Andriy Lunin as Madrid extended their unbeaten league run to 25 games, keeping Barcelona a safe distance behind ahead of next week's Clasico in the Spanish capital.
"It's a very important victory, which brings us closer to the title. We're on a good run and now we're going to think about Wednesday, that we have time to recover well and try to do our best," said Ancelotti.
"Having an advantage before (next) Sunday's game is very important and that was the goal."
Copa del Rey runners-up Mallorca stay in 15th, six points above the relegation zone.
Fantastic Felix
Barcelona, who are desperately trying to force their way back into the title race, matched Madrid's result with a 1-0 win of their own at third-bottom Cadiz.
Joao Felix's clever overhead late in the first half secured the points as coach Xavi Hernandez made sweeping changes to the team that beat Paris Saint-Germain 3-2 in the first leg of their Champions League quarter-final.
The Portugal international led the attack in the absence of the suspended Robert Lewandowski, acrobatically hooking in the only goal after a Cadiz defender's looping header from a corner fell directly to him.
Fermin Lopez had an effort scrambled off the line and Marc-Andre ter Stegen's sprawling save to claw away a Diadie Samassekou piledriver preserved a sixth successive clean sheet in the league for the visitors.
Atletico Madrid completed a good four days as they followed their midweek Champions League victory over Borussia Dortmund with a 3-1 win over third-placed Girona.
Antoine Griezmann scored twice as Diego Simeone's men moved to within four points of their opponents and pulled five clear of fifth-placed Athletic Bilbao in the race for Champions League qualification.
The Basques play Villarreal on Sunday.
Atletico won the home leg of their European tie 2-1 on Wednesday and visit Dortmund for the second leg on Tuesday.
Girona took the lead in Madrid with a fourth-minute goal from close range by Artem Dovbyk that took him on to a league-leading 17 goals.
Griezmann responded by converting a 34th-minute penalty.
Angel Correa then gave the home side the lead six minutes into added time at the end of the first half.
Griezmann extended the lead five minutes into the second half, taking advantage of a defensive error to fire home his 13th league goal of the season.
Girona have lost five of their past eight games and now trail Barcelona by five points.
Rayo Vallecano and Getafe drew 0-0.