Brazilian Everton gave Heracles an early lead from close range after goalkeeper Sander Boschker dropped the ball but after 31 minutes Bryan Ruiz equalised.
Blaise Nkufo and Theo Janssen scored in the 54th and 55th minutes respectively to seal Twente's victory.
Fifth-placed Utrecht dominated against PSV, who finished with 10 men after a double booking for Balazs Dzsudzsak, and created several chances but were denied by the outstanding PSV goalkeeper Andreas Isaksson.
Twente, managed by Steve McClaren, are top with 23 points after nine matches, two ahead of PSV.
Ajax Amsterdam are third with 20 after a 2-2 draw at Roda JC Kerkrade and are level on points with Feyenoord, who beat RKC Waalwijk 3-0 on Saturday.
Luis Suarez converted a penalty to put Ajax ahead and, after Arnaud Sutchuin Djoum and Boldizsar Bodor had given Roda the lead, the Uruguayan salvaged a point with his 12th goal of the season.
Ajax finished with 10 men after a straight red card for Urby Emanuelson nine minutes before time.
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