James Rodriguez headed in late on after Radamel Falcao had missed a penalty as Claudio Ranieri's side hand Paris Saint-Germain the initiative prior to the winter break
Abidal turned Arthur Masuako's cross into his own goal on the half-hour mark before Ducourtioux slotted home from a quick break away in the second half to give the visitors a fully deserved two-goal lead.
Radamel Falcao saw his penalty saved late in the second half before James Rodriguez turned home an impressive header to give his side hope, but Claudio Ranieri's side ultimately slumped to their first league defeat since the loss to Lille in early November.
The visitors started brightly and had the best of the early chances, with Mathieu Dossevi being denied by Danijel Subasic from close range.
Valenciennes continued to impress and earned their reward on 28 minutes. Masuako scuffed a cross into the area after a break from a Monaco set piece and Abidal could only steer the ball beyond the helpless Subasic.
Monaco responded and Layvin Kurzawa saw his finish ruled out for offside before the lively Anthony Martial was denied a penalty after being tripped from behind and Joao Moutinho fired a free kick wide.
Valenciennes made them pay early in the second half, with Ducourtioux collecting the ball in acres of space on the counterattack before calmly slotting the ball beneath Subasic to send the visiting support into raptures.
Falcao spurned the chance to halve the deficit when his tame penalty was saved by the impressive Nicolas Penneteau, but James gave his side some hope when he steered home a clever header following a corner.
The Colombian thought he had snatched a point in the dying minutes but his tap-in was ruled out for offside as Monaco missed out on the chance to move temporarily to the top of Ligue 1 ahead of Paris Saint-Germain's clash with third-placed Lille this weekend.