Alvaro Negredo was the hero for Valencia in La Liga, while Villarreal overcame Athletic Bilbao on Saturday.
Valencia's pursuit of a Champions League position gathered pace on Saturday as Alvaro Negredo struck late to secure a vital 3-2 victory against Almeria.
Nuno Espirito Santo's side looked like losing ground in the race for the top four until Negredo headed in the winner seven minutes from time against the struggling visitors.
The result extends Valencia's unbeaten run to five matches and sees them move into third place, at least until Atletico Madrid face Granada on Sunday.
It was just the Spaniard's second goal since joining the club on loan and followed a frantic first half during which Tomer Hemed twice equalised after goals from Dani Parejo and Rodrigo.
Valencia face fifth-placed Sevilla next weekend, after the Andalusian side take on Malaga on Sunday.
Villarreal's own efforts to qualify for Europe's elite club competition received a boost as they beat Athletic Bilbao 2-0 to climb within a point of Sevilla.
On-loan Real Madrid midfielder Denis Cheryshev's well-taken opener gave Marcelino's men the edge at half-time before Bruno sealed a seventh win in nine league games with a late penalty.
Former Everton and Manchester United manager David Moyes suffered his first defeat since taking charge of Real Sociedad as they were beaten 1-0 by Rayo Vallecano.
Moyes was on the touchline for the first time before beginning a two-match ban, but saw his side stretch their winless run to four after ex-Manchester United man Manucho headed in the only goal of the game from a corner inside the final 10 minutes.
Felipe Caicedo's 90th-minute winner saw Espanyol edge past Celta Vigo 1-0.