The home side were the first to threaten when Alexander Bannink was afforded space and time on the edge of the box, but he fired his effort over the bar.
Ted van de Pavert came within inches of heading De Graafschap into the lead when he powered an effort at goal from Andrew Driver's corner, only to see his attempt cleared off the line.
In the second half, the visitors doubled their lead when Michael de Leeuw raided forward and fired a shot at goal from the edge of the box, and his shot deflected off Van der Pavert and into the bottom corner.
De Graafschap were handed the chance to get back into the game when Kasper Larsen was penalised for handball in the box and a penalty was awarded. Nathan Kabasele took the spot kick and buried his effort past Sergio Padt.
The home side pushed for a leveller late in the game, but Groningen held out to claim the three points. The result lifts the visitors into sixth place in Eredivisie, while De Graafschap remain bottom.