Rooney was making his first start since signing a lucrative new contract – his first since the beginning of October in fact – and his goal will go some way to appeasing the fans upset by his initial stalling over the deal.
He stepped up in the 87th minute to send Allan McGregor the wrong way after Fabio had been nearly decapitated by Steven Naismith’s high boot in the box.
The goal ensured United of their place in the last 16 and resigned Rangers to the Europa League on the night Valencia hammered Bursaspor in Spain.
All the pre-match talk surrounded Rooney and the England striker almost wrote the headlines before half-time when he headed against the crossbar from Fabio’s near-post cross.
It was by far the closest anyone came to breaking the deadlock in a game that was better than the goalless meeting between the two sides in September – but only just.
Rangers routinely had seven men within an imaginary five-yard line to the most advanced United forward, which offered their visitors hardly any room.
On the single occasion United’s skill got them through, thanks to intricate passes from Ryan Giggs, Nani and Michael Carrick, the chance went begging when Nani drove his first-time effort over with what looked like a toe-poke.
Rangers did cause their opponents some anxious moments at the other end with Kenny Miller, who once scored a winner for Wolves against these opponents, a threat.
But the Scotland star has not scored at this level of the game in 14 attempts and he sent one header harmlessly wide before shooting at the feet of Edwin van der Sar from a tight angle when a ball across the face of goal for Vladimir Weiss looked a better option.
As Valencia had virtually wrapped up victory by the break against Bursaspor, Rangers knew they needed to win to survive, which might have led to a more enterprising approach.
United were the ones with the extra class, though, and Rooney was not that far away from putting them ahead with a 25-yard free-kick.
Dimitar Berbatov then wasted a decent opportunity, failing to connect properly with a volley that normally would have expected to put McGregor in trouble.
Carrick was next to get a sight of the Rangers goal and he at least tested McGregor with a low shot which the Scotland keeper beat away.
The growing pressure around the home box led to a more enterprising approach from Rangers and Naismith almost profited from some suicidal defending by Jonny Evans, who needed van der Sar to come to his rescue with a brave block.
Impressive in the first meeting, McGregor was an obdurate presence once more and he denied Berbatov’s angled drive with a neat save to his right.
Rooney’s luckless night continued when he blazed a long-range effort over, before heading a Giggs’ cross wide just after Berbatov had a goalbound shot blocked.
It appeared it was not to be Rooney’s night when another opportunity sailed wide but, five minutes from the end, Naismith made a rash challenge on Fabio and offered the striker a chance to start repaying United supporters in the only currency they really care about.