Kevin Strootman's double and the winner from Slovenian Tim Matavz with eight minutes to go rescued PSV, who had been two goals down at half-time after strikes by Jens Podevijn from close range and Niek Vossebelt's sublime curving long-range effort.
Strootman opened his side's account 22 minutes from the final whistle then equalised 10 minutes later with a shot from just inside the box before Matavz grabbed the three points to put PSV on 21 points, one behind Twente after nine matches.
Luc Castaignos put Twente ahead midway through the second half but five minutes later Guus Hupperts levelled.
Vitesse Arnhem, level with PSV having also played nine times, cruised to a 3-0 win at NAC Breda with Wilfried Bony scoring twice in the second half.
Ajax Amsterdam are fourth with 17 points after dropping a two goal advantage as Luis Pedro salvaged a point for Heracles Almelo in the final minute in a 3-3 draw.
An own goal by Ben Rienstra and one from Lasse Schone gave Ajax, in Champions League action against Manchester City on Wednesday, a solid half-time lead.
Mike te Wierik pulled one back for Heracles after 61 minutes but a minute later Tobias Sana restored the two goal advantage before Thomas Bruns and Pedro spoiled Ajax coach Frank de Boer's mood with goals in the final 10 minutes.
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