Vitesse Arnhem remained third following a 4-1 derby win over NEC Nijmegen, who finished the match with eight men after Victor Palsson, Remy Amieux and Ryan Koolwijk were sent off.
PSV have 33 points from 13 matches following their 6-1 thrashing of ADO Den Haag on Saturday with Twente on 30 and Vitesse Arnhem on 28.
Midfielder Willem Janssen gave Twente a flying start when he headed home the opener after two minutes only for Jacob Mulenga to equalise 15 minutes later.
"We have too many problems with scoring to win matches like this," said Twente manager Steve McClaren.
"Conceding only seven goals in 13 matches means that we are hard to play against but in attack our final pass is not sufficient," added the former England boss.
Vitesse Arnhem came from behind to beat neighbouring NEC Nijmegen, who had Palsson, sent off just before the break for a second bookable offence.
He was followed by Amieux, who also received two yellow cards, in the 82nd while a minute later, Koolwijk was shown a straight red for a wild tackle.
Melvin Platje put Nijmegen ahead in the third minute after Vitesse keeper Piet Velthuizen failed to clear a back pass but Wilfried Bony equalised soon after with a well-placed header.
Guram Kashia added another for Vitesse straight after the break before Bony, with his 14th of the season, and Mike Havenaar sealed Vitesse's second home win.
Feyenoord also stayed in touch with the top as they cruised to a 3-0 home win over bottom side Willem II Tilburg with Lex Immers opening the scoring before a second-half double from Graziano Pelle, on loan from Parma, settled the match.
Feyenoord are fifth with 24 points behind on goal difference to Ajax who were 2-0 winners over VVV Venlo on Saturday.