Ayew headed home Mathieu Valbuena's cross in the 46th minute after Lille had been reduced to 10 following Florent Balmont's dismissal on the stroke of halftime.
Marseille have 26 points from 13 games and trail Paris St Germain on goal difference after the Qatar-backed club, who have played 14 matches, demolished Troyes 4-0 on Saturday.
OM will play their game in hand on Wednesday at Olympique Lyon, who missed out on top spot when they slumped to a 3-0 defeat at Toulouse on Sunday.
"Even when down to 10, Lille managed to keep the ball and make it hard for us," OM coach Elie Baup told French TV channel Canal Plus.
"For quite some time we were playing very well without being rewarded. Tonight, we finally managed to convert one of our chances."
The keepers were the first to shine with Steve Mandanda pulling off a brilliant save to parry Marvin Martin's attempt in the eighth minute.
After 13 minutes, Landreau denied Ayew, Mathieu Valbuena and Benoit Cheyrou in a packed goalmouth from close range.
On his Ligue 1 debut after serving the rest of a Premier League 12-match ban, Englishman Joey Barton, on loan from Queens Park Rangers, picked up a yellow card following his first tackle midway through the first half as he stamped on Florent Balmont's ankle – a foul that could easily have drawn a straight red.
Mandanda pulled off another jaw-dropping save from a powerful Dimitri Payet downward header shortly before the interval just before Balmont was sent off for a foul on Mathieu Valbuena as the France forward was running through on goal.
Just one minute into the second half, Valbuena broke down the left flank and his cross was met by Ayew who made it 1-0.
Marseille were then content to keep Lille at bay and Mandanda spared them blushes again when he blocked Nolan Roux's shot from inside the box after the forward had outpaced the defence.
Earlier, Wissam Ben Yedder ended Toulouse's three-match losing run when he inspired a 3-0 home win over Lyon.
The home side dominated throughout and were rewarded for their efforts five minutes into the second half when Ben Yedder headed home at the far post from Franck Tabanou's cross.
Ben Yedder put the result beyond doubt at the end of a sharp counter-attack three minutes from the end with Etienne Capoue rounding things off in added time.
Toulouse, who were second a month ago before their bad run, moved up to seventh with 22 points from 14 games, while Lyon, who have a game in hand, are fourth on 25 points.
Earlier, Girondins Bordeaux also missed out on an opportunity to go top when they lost 1-0 at Montpellier who had drawn their last three league games 1-1.
It was midfielder Remy Cabella who ended the winless streak when he collected a long pass from Romain Pitau before firing a low shot past Cedric Carrasso in the 68th minute to put Montpellier in 12th place with 17 points from 14 games.
Bordeaux came close in the first half but Nicolas Maurice-Belay wasted chances.
The Aquitaine side are fifth with 24 points from 14 games.