The home side's Sloan Privat went from villain to hero by scoring the opener in the 72nd minute after missing a third-minute penalty before Nicolas Benezet fired home in the 89th.
OM had given new coach Michel, who replaced the departing Marcelo Bielsa, a perfect start with last weekend's 6-0 demolition of Troyes, but were far from their best at Guingamp.
Marseille forward Michy Batshuayi, who was dangerous especially after the interval, missed several chances.
Brittany side Guingamp, who lost their first three matches, are 14th with three points behind Marseille on goal difference.
The visitors had got off to a terrible start when Lassana Diarra fouled Jimmy Briand in the box in the first minute but Steve Mandanda saved Privat's resulting spot kick.
OM looked tentative and had to wait until just before the break for a clear chance with Batshuayi shooting just wide.
Privat, however, was more accurate after the interval.
Briand dribbled down the left and got past defender Nicolas Nkoulou before setting up Privat who tapped in from close range to score Guingamp's first goal of the season.
Batshuayi had several opportunities to level but the Belgian was far too casual and Benezet wrapped up the win for Guingamp a minute from time with a 25-metre strike into the bottom corner.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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