Robert Braber had put Willem II ahead in Eindhoven, yet after Depay had missed from the spot, Jurgen Locadia drew the leaders level six minutes from time and Depay spared his own blushes with the winner three minutes later.
It enabled PSV to move up to 52 points from 20 matches, and extend their lead to nine points over champions Ajax Amsterdam, who have a game in hand and travel to Vitesse on Sunday.
Willem II were ahead on the half-hour mark as Braber headed home a corner from Stijn Wuytens at the near post.
Greek goalkeeper Kostas Lamprou was adjudged to have fouled substitute Locadia to hand PSV a chance from the spot 16 minutes from time, but Depay spurned the opportunity and chalked up his fourth miss out of seven penalties in the Eredivisie.
Jerson Cabral struck a post as Willem II went close to extending their advantage, but soon afterwards PSV drew level as Locadia blasted the ball under Lamprou.
Depay brought relief to the Philips Stadion as he grabbed the winner after a header from a corner by teammate Jeffrey Bruma landed fortuitously at his feet.
FC Twente moved up to fourth as Kyle Ebecilio scored the winner three minutes into injury time for a 2-1 victory at home to Cambuur.
Peruvian defender Renato Tapia put Twente ahead 12 minutes after halftime but Martijn Barto looked to have secured a point for the visitors before Ebecilio netted his first goal in four months.
Goals in either half from Albert Rusnak and Tjaronn Chery gave Groningen a 2-0 home win over Go Ahead Eagles.
Slovakian Rusnak's strike was his first for the club since joining from Cambuur in January.
NAC Breda remained second-bottom following a goalless draw at Excelsior Rotterdam.
(Writing by Nick Said; Editing by Ian Chadband)
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