Still without first goalkeeper Lars Unnerstall, FC Twente started with 38-year-old Przemyslaw Tyton for the second time running after Sunday's 2-0 defeat at Ajax. Centre-half Max Bruns also got his second-straight start with Indonesian international Mees Hilgers out with an injury.
NEC, meanwhile, fielded an unchanged XI which beat Heracles Almelo 2-1 on Sunday to clinch a spot in the play-offs.
After opportunities for Michel Vlap and the Eredivisie's top goalscorer Sem Steijn, a first half dominated by the home side was broken open in the 16th minute, when Czech international Michal Sadilek smartly curled a lost ball around the defence and goalkeeper.
FC Twente looked to be cruising towards the final whistle, but a peaceful evening was rudely interrupted when Alec van Hoorenbeeck was sent off right before half-time for taking down Sontje Hansen as the last man.
It didn't take long for NEC to profit from the sending off after the break - midfielder Kodai Sano picked up a loose ball and launched a rocket into the Twente goal in the 47th minute, putting NEC alongside FC Twente.
Vito van Crooij handed NEC the lead not much later, rolling the ball underneath Tyton for the 2-1 in the 56th minute.
The home side fought back quickly when Ricky van Wolfswinkel couldn't finish a counter, but Sem Steijn was there to pick up the rebound and get Twente back in the game in the 63rd minute.
The ten men of FC Twente fought to get back in the game as NEC were given few chances to capitalise further on the situation. A rare NEC outbreak saw Basar Onal escape with Hansen next to him, but Max Bruns was there to block Onal's pass and dismantle a dangerous 2-on-2 offensive.
As extra time loomed, Bryan Linssen came dangerously close to a late NEC winner, but the veteran saw one effort hit the post, and a later back-heel finish get stopped by Tyton.
Down a man for the majority of the game, FC Twente forced extra time in the play-off semi-final and quickly made the most of the opportunity through Younes Taha, who smartly beat youth international Robin Roefs at his near post.
Unable to put FC Twente under any pressure during extra time, NEC Nijmegen fell to the home side after 120 minutes and saw their season come to an end. NEC manager Rogier Meijer, therefore, ended his five-year tenure in Nijmegen with a loss.
FC Twente will face AZ in Alkmaar in Sunday's play-off final. The winner earns a ticket for the second qualifying round of the UEFA Europa Conference League.
View all the match statistics on Flashscore.
