Olinga's goal in the first match of the new La Liga season saw him become the youngest goalscorer in the division's history, Malaga confirmed on their website.
At 16 years, three months and six days old, the Cameroon-born striker also was also Malaga's youngest-ever debutant.
In the game, Celta Vigo's Enrique de Lucas had wasted a number of chances to take the lead for the hosts, back in the La Liga after five years, early in the second half as the former Chelsea midfielder was twice denied by fine saves from Malaga's Willy 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 byline and cut the ball back for Olinga to bundle it into the empty net off his thigh.
Celta should still have snatched a point at the end but Gustavo Cabral somehow smashed the ball against the bar when presented with an open goal to leave the Galicians empty handed.
Sevilla opened their La Liga season with a deserved 2-1 win over Getafe in an occasionally scrappy game at the Estadio Ramon Sanchez Pizjuan.
Goals by Federico Fazio and Alvaro Negredo, the latter from a disputed penalty, within five first-half minutes ultimately proved enough for the hosts.
Alexis, playing against the team from whom he is on loan, headed Getafe back into the game early in the second half but they could not find an equaliser and it was Sevilla who looked more likely to score again, with Ivan Rakitic hitting the crossbar.
Tomer Hemed scored at either end of the match to earn Mallorca a season-opening 2-1 win over Espanyol.
The Israel international was on the spot after two minutes and then pounced on a stray ball with five remaining to render Mubarak Wakaso`s equaliser worthless.
His winner came after Michael Pereira`s drive had come back off the bar, with the 25-year-old rewarded for showing better reactions than the visiting defence.
Saturday's La Liga Fixtures
Sunday's La Liga Fixtures
Monday's La Liga Fixtures
Deportivo vs Osasuna
Rayo Vallecano vs Granada
Real Zaragoza vs Valladoid