Griezmann scored with his left foot into the lower left of the goal after receiving a pass from Carlos Vela.
Apono never came off during the match. The midfielder scored in the 92nd minute, took four shots and completed 40 passes.
Apono demonstrated his rapport with Francisco Montañés throughout the match, and connected with the midfielder for eight passes.
Real Sociedad's Imanol Agirretxe found the back of the net with a right-footed shot strike that came in the 32nd minute.
Los Maños were hindered when Héctor was given a red card in the 22nd minute.
Real Zaragoza have a record of seven wins, 13 losses and three draws this season, which puts them in 16th place, only two points above the relegation zone.
Real Sociedad are holding down a spot in the Europa League in sixth place with a record of 10 wins, seven losses and six draws for 36 points.
Erreala maintained control of the ball for 67.8 per cent of the contest, a testament to their movement and linking play in the open field.
Real Sociedad won 51 duels and 20 headers, which led to seven shots, all of which were on goal.
The four attempts by Agirretxe were the most of any Real Sociedad player.
Alberto De la Bella's 16 passes to Griezmann were the most between any Real Sociedad team-mates during the match.
Los Blanquillos enjoyed possession for 32.2 per cent of the game. Real Zaragoza had 10 shots, including three on target.