Lars Gerson gave the visitors a surprise lead midway through the first half, but Mutu struck back immediately and completed the comeback in the 68th minute. Ianis Zicu added a third to put the game beyond Luxembourg and give Romania their first win in five Group D games.
They stayed fifth in the group, but moved to within a point of Bosnia-Herzegovina and two of Belarus and Albania.
The hosts were stunned in the 21st minute when Gabriel Muresan could only clear Mario Mutsch's free-kick as far as Gerson. The 21-year-old, who plays his club football in the Norwegian second division, fired a left-footed shot back into the top corner from the centre of the area.
Romania were back on level terms three minutes later, though, as Mutu slid a low shot into the corner following Muresan's ball from the right. Luxembourg were frustrating their opponents, who needed a win to stay in touch with the race for second place in the group, but were struggling to create chances.
They had to wait until the 68th minute to take the lead, and again it was Mutu to provided the finish. Gabriel Torje sent in a right-wing cross and Fiorentina striker Mutu headed it high into the net.
Luxembourg almost hit back immediately, but Ciprian Tatarusanu tipped Daniel Da Mota's close-range shot over the bar. Zicu sealed the points for Romania in the 78th minute when he headed home from Razvan Rat's corner.
Muresan had a chance to make it four a minute from time, but goalkeeper Jonathan Joubert saved his shot with his feet.