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 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 pulsating 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. 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
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