After Gignac scored two minutes before halftime, Florent Malouda equalised for the visitors straight after the break but Ayew netted just before the hour and Payet put the result beyond doubt in the final seconds.
The result put Marseille back on top with 38 points from 17 games, just a day after arch rivals Paris St Germain had claimed provisional leadership on 37 points thanks to their 2-1 victory against Nantes.
Olympique Lyonnais are still third on 33 after twice coming from behind to win 3-2 at Evian Thonon Gaillard, Alexandre Lacazette netting an injury-time penalty after Cedric Barbosa had twice put the hosts in front on Sunday.
Lacazette, who also scored Lyon's second goal after Yassine Benzia netted the first, is the league's top scorer on 13 goals. In Marseille, Metz enjoyed the better start and had the first clear chance five minutes from the interval when Steve Mandanda deflected Malouda’s low shot with his foot.
Marseille, however, quickly went ahead when Gignac beat Johann Carrasso with a downward header from Payet's cross.
The visitors, though, were rewarded for their enterprise as Malouda's 20-metre strike took a deflection off Nicolas N'Koulou to beat Mandanda.
In the 59th minute, Alaixys Romao's attempt bounced off Carrasso's left post into the path of Ayew, who poked home the rebound.
Two minutes into added time, Payet flicked the ball into the net after being set up by Rod Fanni at the end of a counter-attack. Strugglers RC Lens and Lille drew 1-1 in the derby of the North on Sunday.
(Reporting by Julien Pretot; Editing by Ian Chadband)
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