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.
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."
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.
