Midfielder Leroy Fer struck after six minutes to put Twente ahead before second half goals from Luuk de Jong and Ola John settled the match.
Ten minutes before time Twente's Peter Wisgerhof was sent off for a last-man foul but Wilfried Bony missed the penalty. Nacer Chadli made it 4-0 before Mike Havenaar scored a consolation goal.
PSV remain top with 45 points after 22 matches on goal difference ahead of Alkmaar. Heerenveen, 1-0 winners over NAC Breda on Friday, are third with 43, one ahead of Twente who have a game in hand.
South Korean Suk Hyun-jun opened the scoring for Groningen against PSV after 29 minutes finishing unmarked in the area and Leandro Bacuna doubled the lead early in the second half.
After PSV's Stanislav Manolev received his second booking Suk scored his second to seal the victory.
Alkmaar were reduced to 10 men after 15 minutes when Fin Niklas Moisander received a red card for a last-man foul before Alexander Gerndt converted a penalty to open the scoring.
Six minutes later Gerndt made it 2-0 and before the interval Edouard Duplan added a third.
Sixth placed Ajax Amsterdam moved to 40 points after a 4-1 win over NEC Nijmegen with Dmitry Bulykin scoring twice.
