Carlos Vela's goal after just 10 minutes decided the game for Sociedad as they recorded only their second win in their last six league matches, but one that lifts them to within touching distance of fourth-placed Athletic Bilbao.
While Sociedad are well in contention for a second successive top-four finish this season, things are looking a lot bleaker for a Malaga side who themselves claimed a Champions League spot just two years ago.
Monday night's defeat was their 12th of the season and left them in 17th spot in the standings and just three points above the relegation places.
Sociedad made much the better start at La Rosaleda and Haris Seferovic and Vela had already tried their luck with efforts on goal before the latter put the visitors ahead.
Antoine Griezmann and Jose Angel Valdes combined well down the left and the defender's low ball into the box was turned home from the near the penalty spot by Vela.
That ended up being the match-winning strike, with Malaga pushing hard for an equaliser but coming up short.
Sacha Iakovenko twice failed to seriously trouble Claudio Bravo with shots before the break while Sergi Darder also failed to beat the Sociedad keeper on the stroke of half-time.
It was a similar story after the interval with Vitorino Antunes and Nordin Amrabat firing wide before Bravo was called into action again twice in quick succession with 15 minutes to go to deny Roque Santa Cruz.
Substitute Santa Cruz also had one late chance to try and salvage a draw for the hosts but his stoppage-time shot was blocked by David Zurutuza and Sociedad could celebrate the victory.