After Lars Gerson gave Luxembourg a shock lead on 21 minutes Mutu slipped through the visitors' poor defence to score in the 23rd and 65th minutes and Ianis Zicu got the third 12 minutes from time.
After losing 2-1 in Bosnia on Saturday Romania remain a long shot to scrape through. They have five points and lie fifth in the six-team group. France lead the way with 12 points, Belarus and Albania have eight and Bosnia seven.
"It is critical that the ball reaches me," Mutu told state television TVR 1. "In Bosnia, I didn't even touch it.
"While we have a mathematical chance (to qualify) we still believe in it."
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