Andre Villas-Boas' side climbed to fourth in the early table after recovering from falling 2-0 behind to Wissam Ben Yedder's double in the first half an hour.
"It's four goals away from home, it's good. And with the victories, confidence is coming back," Dimitri Payet, who scored Marseille's third goal, told Canal+.
Monaco, who only narrowly avoided relegation last term, remain second-bottom with just two points from their opening five matches and have already conceded 14 goals.
The pressure is once again mounting on coach Leonardo Jardim, who was sacked early last season before returning after an ill-fated spell in charge from Thierry Henry.
Marseille are now only two points adrift of reigning champions and leaders Paris Saint-Germain, and behind Rennes and Nantes on goal difference.
"Maybe we've dared to play a little more," added Payet. "In the last quarter of an hour we suffered too. It's not always nice to watch, but you have to know how to be efficient."
Monaco grabbed the lead in the 17th minute after Bouna Sarr inadvertently handled a ball over the top towards Islam Slimani, with Ben Yedder stepping up to slam home the penalty and score his second goal for the club since joining from Sevilla.
Ben Yedder wasted little time in netting his third, latching onto Slimani's perfectly-weighted through ball nine minutes later, before slotting into an empty net after his initial effort was kept out by Marseille goalkeeper Steve Mandanda.
But the away team hit back as Argentinian striker Benedetto scored for the third straight game.
They were level three minutes before the break, as Valere Germain ended a seven-match goal drought with a back-post diving header.