The 1-0 scoreline has moved visiting Bilbao up to fifth position, six points adrift of fourth-placed Villarreal.
Clear openings were few and far between during the first half, with two of the best falling to Malaga's attacking midfielder Juanpi.
With 12 minutes on the clock the Venezuelan saw his strike from the edge of the box tipped to safety by Bilbao goalkeeper Gorka Iraizoz, while 14 minutes later he fired over from close range following a swift counter-attack.
However, there were no such problems in front of goal for Garcia with 53 minutes on the clock. The Malaga defence failed to react to Ander Iturraspe's corner, leaving the 29-year-old with a routine finish.