Lyon took an early lead when Swedish midfielder Kim Kallstrom volleyed the ball into the right side of the net from just outside the penalty area after Miralem Pjanic's corner after three minutes.
Debrecen were rattled again on 13 minutes when Bosnian Pjanic curled in a delightful free-kick and 11 minutes later he crossed for Sidney Govou's header to make it 3-0.
It took 34 minutes for the Champions League newcomers to threaten the opposition when Peter Czvitkovics shot from outside the box, forcing Hugo Lloris into a good save.
Bafetimbi Gomis scored the fourth with a brilliant lob six minutes after the break.
Debrecen coach Andras Herczeg admitted his side, playing their first ever home game in the Champions League group stages, failed to regain their composure after the loss of two early goals.
"We started poorly and were two goals behind after just 13 minutes. Lyon really showed the difference between the two teams, while our confidence got a hit.
"We knew that could happen to us right after the draw, but our objective for the game against Fiorentina is to make that match a tighter encounter."
Lyon counterpart Claude Puel, whose side sit pretty at the top of group E after two straight wins, was sympathetic with Debrecen's steep learning curve.
"Our opponents lacked experience at this level but I think they must profit from these type of games, even if they lose heavily, in the future," he told reporters.
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