Utrecht won 3-2 on aggregate after taking the first leg 2-0.
Dusan Tadic opened the scoring for Twente after 34 minutes, coming in from the right wing with a superb long drive in the upper corner of the goal. Two minutes later Nacer Chadli repeated the same move from the left to double the lead.
Utrecht pulled one goal back 20 seconds into the second half as defensive blunders from keeper Sander Boschker and Felipe Gutierrez allowed Edouard Duplan to score into an empty net.
"This is a crown on a fantastic season but it was very tough today as we allowed them back into the match through two fantastic goals they scored," Utrecht winger Cedric van der Gun told Eredivisie Live TV.
"But we set it straight during halftime and were a bit lucky with our goal."
For Twente the elimination finishes off a disappointing season in which they topped the table for the first 11 rounds but fell apart after the winter break when manager Steve McClaren was sacked.
Twente failed to qualify for European football for the first time since 2005.