A wonder strike from Luis Alberto rocketed the Romanian champions towards the knockout stage, but victory for Galatasaray over Braga in the night's other Group H fixture meant Paulo Sergio's side were robbed of a runners-up spot behind Sir Alex Ferguson's Red Devils.
A positive result for Cluj was always on the cards in midweek, with United already assured of progression as group winners and in the enviable position of being able to make sweeping changes to their starting XI with one eye on a crucial Premier League derby date with Manchester City on Sunday.
With there nothing riding on the game for the hosts there were a number of empty seats to be seen inside the Theatre of Dreams, with one of them in the dugout - with Ferguson opting to enjoy the company of his chief executive David Gill in the stands rather than take his usual place on the bench.
The first half offered little for those in attendance to get excited about, with defensive errors offering up the only real opportunities of note.
A flurry of activity midway through the half saw a Nick Powell effort blocked, after Cluj keeper Mario Felgueiras had flapped at a Phil Jones cross, and a heavy touch from Tom Cleverley deny him a clear run on goal.
Sandwiched between those efforts, Scott Wootton put in an important last-ditch block to slam the door in Modou Sougou's face.
As the opening 45 minutes drew to a close, United really should have got their noses in front, but Wayne Rooney saw a clever chip beaten away by Felgueiras and Chris Smalling somehow nodded wide of a gaping target from three yards out - before Cleverley was forced off with an untimely knock.
The second period looked to be following a similar theme to the first until Alberto brought the game screaming to life.
Paul Scholes, on for the unfortunate Cleverley, surrendered possession in uncharacteristic fashion and was made to pay by Alberto as he picked the ball up 25 yards from goal and sent an unstoppable drive past the outstretched hand of David de Gea and in off the post.
Everything was going to plan for the men from Transylvania at that stage, with Galatasaray trailing in Portugal.
The Turkish outfit were, however, to turn their tie on its head, making events in the final 10 minutes at Old Trafford irrelevant - with United prepared to turn their attention towards more important challenges to come and Cluj left to contemplate the consolation prize of a place in the Europa League.