Enrique de Lucas had wasted a number of chances to take the lead for the hosts, back in the top flight after five years, early in the second-half as the former Chelsea midfielder was twice denied by fine saves from Will Caballero and also chipped wastefully wide when clean through on goal.
Manuel Pellegrini's changes gave Malaga an extra gear and two of the subs combined for the goal seven minutes from time as Diego Buonanotte got to the by-line and cut the ball back for Olinga to bundle into the empty net off his thigh.
Celta should still have snatched a point in stoppage time but Gustavo Cabral somehow smashed the ball against the bar when presented with an open goal to leave the Galicians empty handed.
Malaga's financial difficulties over the summer meant they lined-up with no new faces, but that continuity from last season appeared to give them the advantage in the early stages as they started brightly.
Javi Varas had to be alert to turn away Joaquin's free-kick and Isco should have scored on 20 minutes when he blazed over after more good work down the right from Joaquin.
Slowly though Celta started to work their way into the game and could have been ahead themselves before the break as Andres Tunez headed a good chance wide and Alex Lopez saw his fierce effort deflected just over.
De Lucas then had three clear openings within the first eight minutes of the second period but Caballero stood tall to block his first two efforts before doing just enough to put the Celta midfielder off and he flicked his third opportunity just wide.
Olinga appeared to have wasted his chance for glory with 13 minutes remaining when Isco's thunderous shot rocketed off the crossbar and fell perfectly for the Cameroonian only for him to scoop the ball harmlessly over.
However, six minutes later Olinga was on hand to turn the ball in when Buonanotte pulled it back into the danger area after the youngster's original effort had come off the post.
Celta desperately pushed forward in search of an equaliser and they should have found it in the dying seconds when De Lucas' clever backheel picked out Cabral inside the area but the centre-back went for power rather than precision and his effort bounced off the bar and away to safety.