A superb second-half strike from the visitors was enough to hand them a famous victory at Old Trafford as Sir Alex Ferguson's men slumped to defeat in their final group fixture
CFR Cluj, meanwhile, arrived at Old Trafford safe in the knowledge they could finish no lower than third in the group, and the Romanians comfortably held their own in a first half which saw chances for both sides but no goals.
Indeed the visitors had the best of the early openings. Midway through the first half Madou Sagou was put clean through on goal but was denied by a superb challenge from Wotton who slid in at the crucial moment to block his shot and force the corner.
Minutes later and the action switched to the other end as Tom Cleverley had an excellent chance to open the scoring. With Danny Welbeck closing down the Cluj defence and managing to nick the ball away, the possession switched to the midfielder but his heavy first touch allowed goalkeeper Mario Felgueiras the chance to come smartly off his line and block his shot.
With half-time looming, United improved and carved out another excellent opportunity. After Felgueiras had saved well from Welbeck and Rooney, United kept the momentum alive and found Smalling from a corner but he could not direct his header on target from close range as the first half ended goalless.
CFR Cluj began the second half in determined fashion and took the lead after just 10 minutes as United fell behind, as has been the case so often this season so far.
Substitute Paul Scholes, who replaced Cleverley at the end of the first half, gave the ball away which eventually fell to Luis Alberto. The midfielder was allowed to take a few touches before unleashing an unstoppable shot which flew into the top corner from fully 25 yards.
With United struggling to work Felgueiras in the CFR Cluj goal, Sir Alex brought Federico Macheda on for Nick Powell with 20 minutes remaining to add some attacking impetus.
Yet for all United's efforts they found it tough going against a CFR Cluj side content to hold their lead. Felgueiras in the visitors' goal in particular was in commanding form, alive to any danger, and always quick off his line to deny any potential goalscoring opportunities.
Whilst the result mattered little to United, it did to CFR Cluj who despite recording a famous win at Old Trafford still exit the competition. A win for Galatasaray in Braga in the other game in the group, enough to relegate the Romanians to the Europa League.
Manchester United, meanwhile, head through as group winners but will now turn their attentions back to domestic matters and the small matter of a trip to Etihad Stadium to face Manchester City.