Eurosport - Wed, 27 Jan 21:55:00 2010
In the second minute of injury-time, Rooney headed Ryan Giggs's cross past Shay Given for his 21st goal of the season after City thought they had forced extra time through Carlos Tevez's third goal over the two legs against the club he controversially left in the summer.
Bellamy was hit on the head by a coin and narrowly missed by a bottle in the passage of play before United's opening goal, in an emotionally charged atmosphere not helped by a war of words between Tevez and United defender Gary Neville.
As expected, United started the game looking for an early goal, pressing forward at all opportunities but faced with a wall of Sky Blue as City sat back and looked for the break.
The counter-attack policy seemed more effective: Rio Ferdinand - playing after appealing his FA charge for violent conduct - nudged Tevez off the ball after his mazy dribble put him clean through, while Edwin van der Sar acrobatically saved Tevez's diving header.
Given was barely tested, keeping out Giggs's drive with ease and snuffing out the danger when Dedryck Boyota's slip nearly let Rooney through.
The second half started in reverse fashion, with City coming out all-guns blazing and Micah Richards forcing a save from Van der Sar with a left-foot drive.
Then, on 50 minutes, came the Bellamy incident. The Welshman was ultimately unhurt by the coin and one positive outcome is that the bottle - which contained liquid and could have done serious damage - missed.
From the next move the hosts took the lead in fortuitous circumstances.
A superb ball from Rooney freed Giggs but he was forced wide by Given and had to play the ball back to Nani. The Portuguese winger lost the ball but Carrick, impressive in an advanced midfield role, knocked it back to Scholes, who rifled a low drive that was deflected into the bottom left.
United regained their impetus after that and City did well to survive a couple of slick moves, including a goal-mouth scramble that saw Rooney inadvertently block a Carrick shot and Rooney denied a simple finish by Boyata's sliding challenge.
They made it 2-0 on 71 minutes when, after a quickly-taken throw found its way to Fletcher, Carrick latched on to the loose ball to side-foot into the bottom left from 12 yards.
Rooney, the Premier League's top scorer with 19 goals in 22 matches, missed a sitter when he put Patrice Evra's low cross wide from close range, and it could have been a huge error had he not atoned in injury-time.
Three minutes later, Tevez - who scored both of City's goals in the first leg - pulled one back to level overall with an audacious flick as he spun around Ferdinand to send Bellamy's cross into the bottom left.
With nine minutes left, Carrick missed a great chance to put the tie to bed when he fired wide after the ball broke kindly to him near the penalty spot, while Given seemed to have forced extra-time when he pulled off an incredible save to bat out Fletcher's point-blank header.
But Roberto Mancini's side failed to clear their lines from the poorly-taken short corner that followed, allowing Giggs to pick out Rooney who headed past the Ireland keeper, rooted to his line as the ball nestled in the left-hand side of the goal.
United face Aston Villa in the final at Wembley Stadium on February 28.