Sunday's narrow victory for second-placed Madrid kept some pressure on leader Barcelona.
Mbappé, serving a red-card suspension, was jeered by many fans at the Santiago Bernabeu stadium four days after he had already been booed in Madrid's 2-1 second-leg loss to Arsenal in the quarter-inals of the Champions League.
The Spanish heavyweights were eliminated 5-1 on aggregate from a competition they have won a record 15 times.
"We did well today," Madrid coach Carlo Ancelotti said. "We wanted to win again and rebound from the elimination. The team came through and Fede (Valverde) was key. This victory gives us a boost."
Valverde scored with a well-placed shot into the top corner from the right edge of the penalty area three minutes into second-half stoppage time.
The Bernabeu was mostly behind the team on Sunday, but some fans jeered when Mbappé was shown in the stadium on the large video screens.
Vinícius Júnior, who also struggled on Wednesday but impressed on Sunday, had a goal disallowed around the 80th because of an offside by Endrick in the buildup as he reached 200 wins with Madrid.
Jude Bellingham, playing in a false-nine position in attack, also performed well for Madrid, who face Barcelona in the Copa del Rey final on Saturday in Seville.
"He played well in that position," Ancelotti said. "We have done well with the formation in the past."
The victory moved Madrid back within four points of Barcelona, who rallied to defeat Celta Vigo 4-3 on Saturday. Third-placed Atletico Madrid stayed 10 points off the lead after losing 1-0 at Las Palmas on Saturday. Fourth-placed Athletic are six points behind Atletico.
Fifth-placed Villarreal, five points behind Athletic with a game in hand, were held to a 2-2 draw with midtable Real Sociedad.
Athletic, who had only one attempt on target at the Bernabeu, were coming off two victories in a row in all competitions.
Midtable Osasuna won 3-2 at last-placed Valladolid, which has lost 12 of its last 13 matches. Osasuna has won two in a row after nine matches without a win across all tournaments.
Sevilla, sitting in 15th place, drew 1-1 at home against 18th-placed Alaves.
