Reims won away from home for the first time since returning to Ligue 1 as Nancy's resurgence was halted.
The Lorraine side had won their last two games, their first league wins since the opening day of the season, and took the lead this evening through defender Sebastien Puygrenier on the half-hour.
But goals from Floyd Ayite and Odair Fortes in the second half turned the game around and Gaetan Courtet had a late third disallowed.
Nancy started well and Romain Grance drew a sharp save from Johny Placide before the hosts opened the scoring.
Thomas Mangani swung in a corner which caused problems for Placide. The goalkeeper got a hand to Salif Sane's header at the near post but captain Puygrenier turned the ball home.
Grange could have doubled the advantage before half-time following good work by Lossemy Karaboue, but Placide blocked his shot.
And Reims were back on terms just three minutes into the second half, when Diego set up Ayite to curl in a shot from the edge of the box.
Ayite then turned provider for the second goal nine minutes later. Courtet and Grzegorz Krychowiak combined to free the forward down the left flank and he crossed for Fortes, who supplied a simple finish to a sparkling move.
Gregorini was forced to beat away another effort from the impressive Ayite as the visitors took complete control after the interval.
And only an offside flag prevented Courtet from putting the seal on victory in stoppage time.
The two goals were enough to lift Reims out of the relegation zone, where they were replaced by Evian, and up to 16th. Defeat saw Nancy return to the foot of the table after Troyes' draw with Sochaux.