The Cameroonian striker, from Malaga's youth team, came on as a second-half substitute and bundled the ball in off his thigh from close range in the 84th minute.
Olinga passed Athletic Bilbao forward Iker Muniain in the record books, Malaga said on their website. Muniain was 16 years and 289 days old when he netted in La Liga in October 2009.
Delayed payments to players, the sales of Santi Cazorla and Salomon Rondon, the team's top scorer last season, and rumours that their Qatari owners were considering selling the club have overshadowed their preparations for the new campaign.
Malaga coach Manuel Pellegrini said a draw would have been a fair result, but preferred to switch his attentions to Wednesday's venture into Europe.
"The group had to endure some difficult moments and this will help strengthen minds and team spirit," the Chilean told a news conference.
"Now we have to think about the Champions League tie against Panathinaikos."
