Valencia secure Champions League spot
Real's second and third goals were scored by Cristiano Ronaldo, his 37th and 38th in the league this season and 50th and 51st in all competitions.
His league tally equals the record jointly held by former Real striker Hugo Sanchez (1989/90) and former Athletic Bilbao forward Telmo Zarraonandia, known as Zarra (1950/51), and he has one more match next weekend in which to set a new best.
Valencia have 68 points from 37 matches, six ahead of Villarreal, who are assured of fourth and go into the qualifying round for Europe's elite club competition.
Second-placed Real are 21 ahead of Valencia and four behind Barcelona, who were crowned champions for a third straight season on Wednesday and showed off the trophy to their fans at a festive Nou Camp after a 0-0 draw with Deportivo La Coruna.
Valencia coach Unai Emery said he was not sure whether he would continue in his post next season despite securing the club's second third-place finish behind Barca and Real in a row.
"If coming third and going into the Champions League does not inspire then there is something missing," Emery said at a news conference.
"It will be difficult to overcome Barcelona and Real Madrid but you have to keep faith that it's possible."
Athletic Bilbao, Sevilla and Atletico Madrid made sure of places in the Europa League as eighth-placed Espanyol lost 1-0 at Real Zaragoza to fall out of contention.
Zaragoza clung on to their top-flight status but remain in the final relegation place and in danger of following Almeria and Hercules down to the second division.
Bilbao drew 1-1 at home to Malaga, Sevilla beat visiting Real Sociedad 3-1 and Atletico won 2-1 at home to Hercules to leave all three on 55 points with one game left.
Atletico coach Quique Sanchez Flores bade farewell to the home fans in his last match at the Calderon before he bows out when his contract expires at the end of the season.
His final days in charge have been overshadowed by a breakdown in his relationship with Uruguay striker Diego Forlan, whom he left out of the squad for Sunday's game.
"It has been a very difficult week, with a spectacular mess that nobody wanted, but it was been resolved naturally and well," Sanchez Flores told a news conference. "The team secured its objective and has qualified for Europe."
Atletico's Madrid rivals Getafe remain precariously placed despite beating Osasuna 2-0 at their Coliseum stadium and are level on 43 points with Depor, one ahead of Zaragoza.
Getafe play at Real Sociedad next weekend, Depor host Valencia and Zaragoza play at Levante. Real Mallorca, who lost 3-1 at Almeria, Sociedad and Osasuna all have 44 points and could still be relegated.