Barely a minute in, Brest had a golden opportunity to take the lead, as Mathias Pereira Lage’s flicked header found Abdallah Sima, who bore down on goal, but saw his close-range effort from an angle saved by Geronimo Rulli.
However, Marseille quickly settled into the contest thereafter and went in front on eight minutes as Luiz Henrique’s superb switch of play found Gouiri in space, with the former Nice attacker steadying himself before drilling into the far corner past Gregoire Coudert.
For a period in the first half, L’OM were in control without often threatening to double their advantage, and they were ultimately punished for that lack of attacking intensity when Kenny Lala’s cross ricocheted off Adrien Rabiot and looped out unexpectedly for a corner.
The resulting delivery by Pereira Lage was then headed against the crossbar by visiting skipper Jeremy Chardonnet, with Ludovic Ajorque’s follow-up blocked by Rulli before Sima made amends for earlier by tucking in the rebound.
The Stade Velodrome faithful were on their feet again, though, on 37 minutes when, following a free-kick routine involving Pierre-Emile Hojbjerg and Rabiot, the ball was played to Mason Greenwood, who shifted it onto his right foot and lashed it in from around 25 yards via a huge deflection off Chardonnet.
And things got even better for Marseille approaching the break, as Greenwood turned provider, lofting a cross into the path of Gouiri, who chested it up in the air and perfectly executed a stunning overhead kick.
The second half began much more sedately, but Marseille did put the outcome beyond doubt on 63 minutes as Gouiri beat the offside trap to slot home Rabiot’s through-ball and complete his treble - a goal ultimately confirmed by VAR after initially being denied by the linesman’s flag.
Gouiri soon departed the pitch to a standing ovation as he was replaced by Jonathan Rowe, with De Zerbi’s men easing their way to victory despite some defensive sloppiness to move two points clear of Lille, who are now third.
Lille happen to be Marseille’s next opponents next Sunday as the fight to finish in the top three and automatically qualify for next season’s UEFA Champions League intensifies, while Brest host already-relegated Montpellier earlier that day, looking to avoid successive home defeats in Ligue 1 for the first time in more than two years.
Flashscore Man of the Match: Amine Gouiri (Olympique de Marseille)