The former Arsenal man swooped after just 10 minutes at the Estadio La Rosaleda to send his team level on 40 points with fifth-placed Villarreal.
That pair are four points off Athletic Bilbao in the fourth and final Champions League spot at the completion of round 24 of this season's La Liga campaign.
Both Villarreal and Athletic had dropped to defeats over the weekend.
Conversely, results have gone against Malaga and Bernd Schuster's struggling side - who have now lost 12 times this season - find themselves in 17th, just a place and three points off the relegation zone.
Vela turned in what proved to be the match winner from around the penalty spot after good work down the Sociedad left by Antoine Griezmann and Jose Angel Valdes.
Malaga responded well enough to going behind but, despite efforts from Sacha Iakovenko and Sergi Darder before the break and Vitorino Antunes and Nordin Amrabat after it, they could not find a way back.
Roque Santa Cruz was denied twice late on by Sociedad keeper Claudio Bravo and the Paraguay striker then had a shot blocked in stoppage time as the visitors held on for all three points.
- Sports & Recreation
- La Liga
- Athletic Bilbao