Rooney slotted home a pair of second-half penalties to give the visitors their first Group C win, although skipper Nemanja Vidic will miss the remainder of the group phase after being sent off for a high tackle on Gabriel Giurgiu.
The goals, which took Rooney to 26 in the competition on his first start since being sent off in Montenegro and suffering a ban Sir Alex Ferguson fears will prevent him from featuring at Euro 2012 and the win should put a smile back on the striker's face as United have now moved into second spot in Group C.
However, Ferguson will be less than impressed with the overall performance.
After tossing away a two-goal lead against Basle at Old Trafford three weeks ago, United could not afford to take this game lightly as Sir Alex Ferguson might have expected when the draw was made.
It was not a surprise that Ferguson made nine changes from the team that drew at Liverpool on Saturday.
But if anything, this one was stronger, with Rooney, Javier Hernandez and Vidic amongst those returning.
However, if the Red Devils chief had expected the wasteful ways to be eradicated, he was sadly wrong.
Time and again United squandered possession under little pressure.
At one stage, the normally dependable Vidic was guilty of simply passing the ball to a member of the opposition side close to his own area.
Bratislav Punosevac immediately drilled an effort towards goal which Anders Lindegaard gathered.
Lindegaard was culpable minutes later when he smacked a clearance straight into Vidic.
The Dane was fortunate Punosevac was moving in the opposite direction to the one the ball rebounded into, otherwise the Otelul striker would have tapped into an empty net.
Without a point so far and their own president suggesting avoiding embarrassment was their only target, Otelul visibly grew in confidence.
And Liviu Antal came closest to breaking the deadlock a minute before the break when he guided a close range header over.
It all must have come as a massive disappointment for Ferguson.
Clearly the technically superior team and enjoying an overwhelming advantage in possession, United did little with it.
Rooney did not get into the contest for half an hour, by which time Patrice Evra had embarked on a forceful burst to draw a decent save out of Branko Grahovac.
Like their hosts, United's clearest opening in the opening period came in its' death throes as Nani rolled a pass into Michael Carrick's path.
It was an inviting opportunity that Carrick wasted by blazing over, typifying much of his side's overall sloppiness.
For the first 15 minutes of the second half it would not be unfair to say nothing happened, except for a string of yellow cards, two for fouls on Nani.
It all livened up on the hour though, starting with a low Nani cross to Rooney, whose shot on the turn bounced narrowly wide.
The pair combined on United's next attack too, this time to provide Rooney with space from which to pick out Hernandez.
Sergiu Costin instinctively stuck out an arm to prevent the cross reaching the Mexican.
Costin was fortunate not to be sent off. Instead, the spot-kick proved to be United's only reward as Rooney sent Grahavac the wrong way.
Once in front, it was hard to see how the visitors could not win.
Within minutes Otelul were back in it though thanks to a second tough call on United by German referee Felix Brych, who decided there was an element of danger about Vidic's challenge on Giurgiu and promptly sent the Serbian off.
Vidic was stunned. Ferguson reacted by introducing Jonny Evans and Phil Jones to repel a growing wave of home attacks.
Costin headed over, then Punosevac's shot on the turn almost crept in.
Their hopes were ended by the dismissal of Milan Perendija for a second bookable offence two minutes from time, after which Rooney struck again finding the same corner as previously after he had been tripped by Liviu Antal.