Just minutes after Twente got denied a penalty by referee Rob Dieperink, the visitors got dealt a blow when Adam Kaied fired NAC in front with a curled effort in the fourteenth minute.
Nearly immediately after, Elias Mar Omarsson punched in his sixth goal of the campaign as the Icelandic striker skillfully put away a sailing cross from Boy Kemper.
FC Twente knew what was asked of them and turned up the heat on NAC's half, but Michel Vlap, Bart van Rooij, and Mathias Kjolo all failed to find the net before the break.
The in-form visitors carried their pressure on into the second half and created two big opportunities through Vlap and Eredivisie top scorer Sem Steijn, but neither for former nor the latter got Twente back in the game.
Daan Rots cleverly headed in a corner just fifteen minutes before the final whistle, giving FC Twente the opportunity to launch a full-scale last-ditch offense.
The equaliser seemed to followed soon after when former Norwich striker Ricky van Wolfswinkel caught the NAC defense off guard and calmly finished a 1-on-1 with goalkeeper Daniel Bielica, but it got ruled out for offside.
With Twente dominating possession on NAC's half, the Europa League outfit battled for a point and got close one more time in injury time, but Van Wolfswinkel's header from close range missed both the accuracy and power to beat Bielica.
FC Twente became the latest victim to week 19's surprises after PSV, FC Utrecht, Feyenoord, and AZ also lost points in their Saturday fixtures. The visitors missed the opportunity to steal fourth place and will look to regroup before their European trip to Swedish champions Malmo FF.
NAC fought their way back into the top half of the league with a much-needed win after three consecutive losses in the Eredivisie.
