PSV were behind twice and looked to have missed out on victory from a pulsating match when Colin Kazim-Richards struck an 89th-minute equaliser.
However, Depay - the 20-year-old Netherlands international - snatched Phillip Cocu's side an eighth win in nine league outings to restore their four-point lead over second-placed Ajax.
PSV had kept six successive home clean sheets in the league, but it took Feyenoord just 13 minutes to snap that run.
Elvis Manu raced behind the defence, rounded goalkeeper Jeroen Zoet, and though he under hit his attempt on goal, Jeffrey Bruma slipped as he was rushing in to clear and it rolled over the line.
De Jong then equalised nine minutes later following a delightful team move, only for Jordy Clasie to burst through the midfield and set up Karim El Ahmadi, who bent it home with the outside of his boot three minutes before half-time.
De Jong's quick-fire brace just after the hour swung the game in PSV's favour – and left the man who spent the first part of 2014 on loan at Newcastle United - with seven goals in his past five Eredivisie appearances.
Kazim-Richards silenced the home fans, but only momentarily as Depay struck the winner in the final moments.
The result ensured PSV ended a run of three consecutive losses to Feyenoord, who dropped 12 points off the pace.
