With nine goals in their last three matches heading into this fixture, the Enschede club were on the goal trail again after 21 minutes thanks to Felipe Gutierrez.
Luc Castaignos then doubled the lead 11 minutes into the second half, and although Jop van der Linden reduced arrears from the penalty spot soon after, Dusan Tadic put the result beyond doubt after 62 minutes.
The win sees Twente move above Ajax and into second place, level on 33 points with Vitesse, who face NAC Breda on Sunday.
There was also movement at the other end of the table, where basement side NEC Nijmegen beat Roda 4-3 to close within a point of the teams above them.
In a topsy-turvy encounter, Roda put themselves in the driving seat with early goals from Guus Hupperts (eight) and Krisztian Nemeth (12).
However, the home side came out fighting after the interval and Marnick Vermijl found the target immediately with two goals in six minutes from Soren Rieks then edging them ahead.
Kevin Conboy made it 4-2 nine minutes from time and although Frank Demouge’s goal soon after set up a nervy finish, NEC held on for only their third win of the season.
The result means just five points now separate them from PSV Eindhoven in 10th, although they have played a game more than most of the teams above them.
ADO Den Haag are just two points off the bottom after slipping to a 2-1 loss at home to RKC Waalwijk, who leapfrog them in the standings.
Two goals from Kenny Anderson after seven and 82 minutes gave RKC the advantage, with Tom Beugelsdijk reply coming too late to save ADO.