The visitors remain without back-to-back wins since early December after a stuttering midweek victory over Nice.
"I like this match here, there was self-sacrifice, courage and it's very positive," Marseille's interim coach Nasser Larguet, who replaced the suspended Andre Villas-Boas earlier this month, said.
"Marseille is on the right track. The state of mind is very positive."
Nantes, languishing in the relegation play-off place, was dreaming of a second straight win itself when Ludovic Blas put it ahead in the 50th minute, profiting from Marseille goalkeeper Steve Mandanda missing an attempted clearance from Alvaro's tame back-pass.
Payet levelled 19 minutes later and almost snatched a winner, but was denied by a flying save from home goalkeeper Alban Lafont.
Marseille remains in crisis, without a permanent manager and with only two wins in 13 league games, but is level on points with fifth-placed Rennes thanks to a strong start to the campaign.
Talk of a title bid is well and truly over though, with Lyon and Lille both 17 points clear of Marseille in sixth.