Andre Ayew scored from a packed goalmouth 10 minutes into the second half and his younger brother and fellow Ghana forward Jordan added the second two minutes from time as Marseille moved to second place on 22 points.
They trail PSG, who lost 2-1 at home against St Etienne on Saturday, on goal difference but have a game in hand.
Fellow title hopefuls Toulouse were beaten 1-0 by Bordeaux to end the weekend in fourth place, three points behind PSG and Marseille.
Marseille, who had lost their last three games in all competitions without scoring a goal, struggled in the first half before their physical power made the difference.
"It is never easy to come and win here. We did not play a good first half but after the break, we were rewarded for our efforts," Mathieu Valbuena said.
"The most important thing is that we closed the gap on Paris. We saw that they are not invincible, it's a good morale boost."
Valbuena, one of Marseille's best players this season, played his part in his team's success.
Kabore headed into the box for Andre Ayew to poke the ball home.
Valbuena then set up Jordan Ayew in the box, with the Ghana striker shaking off his marker to coolly slot the ball past Ochoa.
Valbuena almost made it 3-0 in the closing stages but Mexico keeper Ocha tipped his attempt over the bar.
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- Andre Ayew