The Argentine midfielder converted Jeremy Morel's low cross from the right in the 51st minute following a closely-contested first half with few scoring chances at the Georgios Karaiskakis stadium.
His strike proved enough to seal all three points for Didier Deschamps's team, who have just three points from five French league matches, as Olympiakos failed to rally in their first competitive outing of the season.
"We showed that we had an appetite for victory," Deschamps told a news conference.
"Victory is always good, especially in the Champions League and coming at a ground where it is often difficult. There is of course a long way to go but victory will give us peace of mind and confidence."
"I do not think that my team has two faces," he continued.
"On Saturday I saw that my players had no will to fight. Perhaps sometimes there are fluctuations but I know my team very well and we showed what we are capable of with this performance."
The hosts' lone striker Kevin Mirallas had the first clear opportunity to score, in the 21st minute, but the Belgian side-footed his effort wide of the post.
Lacking penetration for much of the opening half, Marseille were reduced to trying their luck from a distance through Jeremy Morel and Benoit Cheyrou.
The pair combined in the 35th minute to create the visitors' best opening, however, when Cheyrou headed Morel's cross narrowly over Franco Costanzo's crossbar.
Loic Remy almost opened the scoring for Marseille two minutes later but his shot cannoned off the right post.
Marseille went in front six minutes into the second half when Gonzalez tapped home at the near post from Morel's superb right-wing cross.
The goal stunned the home crowd and Olympiakos could not find a response.
"Certainly it was a disadvantage for us that this was our first competitive match," said Olympiakos coach Ernesto Valverde, whose team face Arsenal in their next match at Emirates Stadium in London in two weeks' time.
"We have said that the clear aim this year is the championship," Valverde added. "The Champions League is something extra, in which we strive to excel.
"Now we have to go to Arsenal and go for a win, although we know how difficult it is. The truth is that in the group we are dealing with three very good teams."
