Rasmus Bengtsson gave his side the lead in the 19th minute before Shadrach Eghan doubled the advantage nine minutes later.
Dusan Tadic's penalty on the stroke of half-time put the game beyond Groningen before Eghan bagged his second in the 54th minute and Jesus Corona rounded off the scoring with five minutes to go.
The win put Twente top on goal difference ahead of PSV and Heerenveen, who won 2-1 at home to Cambuur.
The hosts went in front through Luciano Slagveer's goal in the 17th minute, before Jody Lukoki brought the hosts level 20 minutes in to the second half.
Parity lasted only a minute however, as Alfred Finnbogason's goal extended Heerenveen's unbeaten run to five games.
Vitesse climbed to fifth with a 3-2 win away at winless NEC.
Kelvin Leerdam gave the visitors the lead in the 11th minute before Christoph Hemlein levelled the scores on 33 minutes.
A Theo Janssen penalty gave Vitesse the advantage going into the break before Michael Higdon came off the bench to net a second equaliser for the hosts with five minutes remaining.
It looked as though both sides would have to settle for a point until Lucas Piazon struck in the final minute to give Vitesse their third win in four games.
Elsewhere, seventh-placed Feyenoord ran out 4-2 winners at home to struggling ADO Den Haag.
Graziano Pelle opened the scoring for the home side as early as the seventh minute, before Bruno Martins Indi grabbed a second just before half-time.
Pelle completed his hat-trick with goals in the 54th and 63rd minutes, before Ricky van Haaren and a Jordy Clasie own-goal in the final five minutes took some of the gloss off the scoreline for Feyenoord.
