Sir Alex Ferguson paid tribute to a "world-class" performance from Wayne Rooney after the England striker scored the injury-time winner that sent Manchester United into a League Cup final meeting with Aston Villa.

Manchester United's Wayne Rooney (left) celebrates his goal during their English League Cup second-leg match against Manchester City at Old Trafford on Wednesday. United won 3-1 and advanced to the League Cup final. AP

Rooney's header secured a 3-1 victory over Manchester City at Old Trafford and a 4-3 aggregate semi-final win for United, who have now reached the final of the competition a record seven times under their Scottish manager.

The game was as volatile as the first leg and, among a number of lingering issues, United appear likely to face an investigation by the Football Association after City forward Craig Bellamy was hit by a missile as he prepared to take a corner.

But, as Rooney took his season tally to 21 goals -- following on from the four he scored in the weekend Premier League victory over Hull - Ferguson could not speak highly enough about his club's top performer.

"I thought Wayne was much better today than he was on Saturday and he scored four goals against Hull," said Ferguson.

"His control, his leading of the line and his penetration was absolutely fantastic tonight. It was a wonderful performance and true, world-class display."

On a memorable Old Trafford evening, fueled by an incredible atmosphere which was the legacy of an ill-tempered first leg, goals from Paul Scholes and Michael Carrick put United well in control until Carlos Tevez equalised the aggregate score after 75 minutes.

Rooney's late intervention, however, continued Ferguson's remarkable record in the competition.

"I'm proud of that and proud of the team today," he said. "The supporters were unbelievable and, when they are like that, we never let them down.

"It's a derby game and you like to win your derby games. We've had our fair share since I came here but the atmosphere tonight and the fact it was a semifinal added a lot of spice to the match.

"Scoring so late brought a special type of celebration."

Darren Fletcher, who had a starring role in United's midfield, reflected the delight in the United camp and enjoyed a slight poke at the losers when he described how his team had done their talking on the field.

"It's a semifinal and the win takes us to the final but it was against our local rivals and you can see how much it means to the fans," he said.

"There is great rivalry between the two clubs and we know about everything that went on in the first leg. But it was important for us to go on to the pitch and let our football do the talking.

"It's easy to talk but you have to do it on the pitch and that's what we did tonight."

City manager Roberto Mancini looked bitterly disappointed by the manner of his team's defeat although he believed the performance provided further evidence to back up his claim that City can finish in the top four of the Premier League.

City remain in the FA Cup, where they face a fifth-round home tie with Stoke City, meaning their hopes of appearing in a first major final since the 1981 FA Cup Final are not dead.

"I would like to have won for the fans and for the players," said Mancini. "But now we have Kolo (Toure) and (Joleon) Lescott (coming back), it is possible that we can finish in the top four. For us it was most important for us to play well and get into the final.

"I think that when you lose against United, it is important you can learn. It's too easy to improve when you win, you must do it when you lose. We must work in the next two or three months."