The former Arsenal man scored for the first time in five games, giving his team a vital win in its push for a Champions League berth.
The Mexican attacker cut inside from the right side of the box to finish off a move in the 10th minute. The goal would stand up for the visiting side at La Rosaleda, as Real Sociedad moved to within four points of fourth place and the final Champions League berth.
Vela now has 10 goals in the league in 2013-14, and 15 tallies in all competitions. His career high in league goals was set last season, when he scored 14 times.
The 24-year-old recently announced he would not be featuring for Mexico at the 2014 World Cup, continuing his three-year absence from the national team picture.