Valencia were assured of a top-four finish in the Spanish La Liga and a berth in next season's Champions League after Real Betis lost at Athletic Bilbao.
The defeat left fifth-place Betis eight points behind Valencia in fourth with two games left for the Seville-based club.
Iker Munian headed in a cross from Inigo Lekeu for Bilbao's opener in the 76th minute, and Aritz Aduriz scored from a pass by Inaki Williams in stoppage time.
Betis hit the crossbar twice when pressing for a late equalizer before Aduriz scored on the final kick of the match.
Valencia played later on Saturday, knowing their mission was accomplished, and lost 1-0 at regional rival Villarreal.
Mario Gaspar headed in Villarreal's winner with four minutes left.
Valencia finished in 12th place the past two seasons but rebounded under manager Marcelino Garcia Toral in this campaign.
"We have had a great season thanks to everyone, from the coaches to the staff, which made good signings," Valencia midfielder Dani Parejo said.
"Thanks to everyone, Valencia is back to where it should be."
Champions Barcelona, Atletico Madrid and Real Madrid are also heading back to the Champions League next season.
Villarreal's victory kept them on pace for a Europa League berth.
Elsewhere, Eibar rolled past Girona 4-1 in the first match since Jose Luis Mendilibar agreed to stay on another season at the Basque Country club.
The visitors were in control at the break thanks to a Kike double, only for Aday to halve Girona's deficit early in the second half.
Late goals from Joan Jordan and Takashi Inui secured only Eibar's second victory in 10 games to move them within one point of ninth-placed Girona.
Lucas Perez scored in stoppage time to give the already-relegated Deportivo La Coruna a 1-1 draw at Celta Vigo in the regional derby for northwestern Galicia.
On Sunday, Barcelona host Madrid in the clasico.