Depay came on to score just before the hour mark and break the deadlock as the Netherlands were still being held 1-1 in a match they were expected to win comfortably.
The Manchester United striker rose to head home an inch-perfect cross from club mate Daley Blind from point blank range in the 58th minute to hand the momentum back to the Dutch after Luxembourg had fought back into the match.
Depay then scored his second, bending a free kick over the wall in the 83rd minute to help the Netherlands advance to seven points in Group A, three behind leaders France.
The Dutch had gone ahead in the 36th minute through Arjen Robben, playing his first international in a year.
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Injury had kept Robben out of the team since last November but he suffered another muscle strain before halftime and had to be replaced.
The Dutch then gave away a penalty just before halftime which Maxime Chanot converted.
Luxembourg brought on a 16-year-old substitute Vincent Thill to make his debut near the end of the game but they still lie bottom of the table with only a single point from their four matches.
(Reporting by Mark Gleeson; Editing by Ian Chadband)
