With eight matches remaining, Twente have 67 points, two ahead of PSV, who travel to third placed Ajax Amsterdam (61) next Sunday.
PSV went down 2-1 at NAC Breda on Saturday for their first league defeat since March 15 last year.
Ajax, without suspended top scorer Luis Suarez for the trip to Sparta Rotterdam, had settled the match before the interval after Siem de Jong opened the scoring in the 14th minute and a fine volley by Gregory van der Wiel doubled the lead. Dane Dennis Rommedahl added a third goal after 61 minutes.
Fourth place Feyenoord, on 50 points, extended their unbeaten run away from home to eight matches with a 4-2 win over Roda JC Kerkrade.
Former Roda striker Sekou Cisse scored from close range in the 14th minute. Six minutes later Roda were reduced to 10 men following a straight red card for Ruud Vormer.
Cisse netted his second goal on the hour before Jeanvion Yulu Matondo pulled one back but Luigi Bruins and Roy Makaay settled the match.
Feyenoord goalkeeper Darley was sent off six minutes before time for a professional foul and Boldizsar Bodor scored Roda's second goal from a free-kick.
