The Gelredome outfit are some way below NAC in the league, but they did not let this affect them as the visitors were undone by a late surge from Vitesse.
Emile Mbamba fired Vitesse in front on 33 minutes, but NAC drew level through Rick Versteeg moments before the interval.
Michael Jansen restored Vitesse`s advantage three minutes into the second-half, but NAC rallied bravely and Mark Schenning squared the game shortly after the hour.
Vitesse continued to pour forward and Matthew Amoah fired them in front on 82 minutes.
NAC pressed for a third equaliser, but were hit on the break as Mbamba grabbed his second of the game in injury-time.
The game saw Jan van Halst make his debut for Vitesse, following his move from Ajax.
