Second-placed Twente were looking to keep the pressure on at the top of the table, with Ajax having started the day with a five-point lead.
Twente had lost 3-2 to PSV Eindhoven on Saturday, and they were dealt another blow after just five minutes when a cross from the right found Krisztian Adorjan, whose shot was only partially saved by goalkeeper Nick Marsman and crept over the line to give the hosts a shock lead.
It took Twente most of the first half to get into the game, but shortly before half-time Dico Koppers found the unmarked Youness Mokhtar, whose shot was parried wide by Groningen goalkeeper Marco Bizot.
The second half was a more even contest, with half-chances at both ends.
Twente eventually showed their class and equalised in the 77th minute when Serbian Dusan Tadic scored his 10th goal of the season, after collecting a pass from Luc Castaignos.
That gave the high-flyers a point they just about deserved, although they nearly conceded a late second when Groningen substitute Richairo Zivkovic only just failed to control a ball in the six-yard box, allowing Marsman to smother.
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