With both sides having little to play for, the game started slowly, but it improved improved after the break as Aritz Aduriz and Pablo Hernandez passed up chances to give the visitors the lead.
Instead Sociedad got the winner midway through the second half as Griezmann slid in to meet Xabi Prieto's cross for his third goal in four games to seal a 12th-placed finish for the Basques, their best in the top flight since coming second in 2003.
Valencia were already assured of a third consecutive third place, but Unai Emery still named a reasonably strong side for his last game in charge and they had the better openings in a cagey first period.
Aduriz just failed to direct his header from Jordi Alba's fine cross on target after only two minutes and the former Athletic Bilbao striker came close again toward the end of the half as he turned Alberto de la Bella, but his attempted chip had too much elevation and floated over.
Hernandez then forced Claudio Bravo into his first serious save of the game with a smartly struck shot four minutes after the interval before Aduriz headed over when well-positioned inside the area.
Mikel Aranburu was playing his final game for Sociedad before retiring after 15 years with the club and the midfielder was denied a goal on his farewell as Diego Alves comfortably collected his header just before the hour mark.
The opener did arrive for the hosts five minutes later, though, as Griezmann showed great movement to continue his fine end to the campaign and get just enough on Prieto's driving cross to steer the ball past Alves.
Valencia pushed forward in search of a leveller, but they never looked like finding a way through, although Jonas did fire just over from the edge of the area with two minutes remaining.