Glynor Plet scored a 62nd-minute equaliser for Steve McClaren's men to cancel out Ebi Smolarek's early opener.
The draw was the third time this month Twente has dropped points and left it a point behind leader AZ and level with second-placed Ajax, both of whom have a game in hand.
Viktor Elm scored twice as Heerenveen won comfortably at home to VVV-Venlo to keep up its bid for European qualification next season.
Heerenveen lies fifth in the Eredivisie table after a 4-1 win which also saw Filip Djuricic and Bas Dost score while VVV, whose consolation goal came from Barry Maguire, is in the bottom three.
Roda JC claimed a 3-1 victory over fellow UEFA Europa League play-off contender Vitesse Arnhem.
Sanharib Malki put Roda in front in the 25th minute and Davy de Beule doubled the advantage 12 minutes later.
Davy Propper pulled one back to Vitesse just one minute after that, but Mads Junker got Roda's third four minutes into the second half to end the visitor's hopes.
Nourdin Boukhari was both hero and villain as he scored the equaliser as NAC Breda claimed a vital point against NEC Nijmegen in its battle against relegation before earning a straight red card in the last minute.
Lasse Schone put the visitor ahead in the 20th minute before NAC forced its way back into the game with Boukhari claiming a deserved equaliser.
The Moroccan undermined his good work when he was sent off for a rash challenge, just four matches into his second spell with the club.