Getafe's 1-0 win over Malaga condemned last-place Real Betis to relegation, while Rayo Vallecano scored three times in the second half for a 3-0 win at 10-man Granada.
Getafe's second win in 2014 left Betis in last place and an unreachable 13 points from safety with only four games to play.
Forward Adrian Colunga scored what proved to be the winner seven minutes into the game at Getafe from a pass by Ciprian Marica, who left his side a man down from the 37th for a second yellow card.
But Malaga couldn't take advantage of the extra man and itself lost a player when Marcos Angeleri was sent off for a second booking in the 76th.
''This victory is huge,'' Getafe coach Cosmin Contra said. ''You saw team spirit today. We are still alive.''
Rayo rose into ninth place with only one loss in its last 10 matches. Rayo held Granada in check in the first half before Yacine Brahimi's dismissal for a second yellow card in the 51st turned the match in the visitors' favor.
All the matches observed a minute of silence before kickoff for Barcelona's former coach, Tito Vilanova, who died on Friday after a battle with cancer.
