Andre Villas-Boas' men could only extend their lead over third-placed Rennes, who host Montpellier on Sunday, to nine points.
Runaway leaders Paris Saint-Germain sit 12 points clear of Marseille, but have seen their game at Strasbourg, scheduled for Saturday, postponed due to fears over the coronavirus.
Marseille have only lost once in their last 17 league games as they chase a return to the Champions League group stage for the first time since 2013, but they stumbled badly against Amiens.
The home side grabbed the lead in added time of a largely drab first half, as Morgan Sanson's smart turn created space for a shot which Amiens goalkeeper Regis Gurtner allowed to fly past his feeble attempt at a save.
Dimitri Payet continued his fine season by scoring his 12th goal of the campaign just before the hour mark, gliding past two defenders before seeing his effort deflected past the stranded Gurtner.
There was further reason for Marseille fans to cheer late on, as star winger Florian Thauvin came on as a replacement for Payet to make his first appearance since September 1 after ankle surgery.
But the evening turned sour for the home crowd, as Serhou Guirassy scored from the penalty spot with seven minutes remaining to set up a grandstand finish.
And Iranian substitute Saman Ghoddos bundled in from close range in the 96th minute to boost second-bottom Amiens' slim hopes of avoiding relegation.