The home side dominated at Anfield but goals from Nigel de Jong and Edin Dzeko kept Roberto Mancini's team in the tie until the superb Welsh striker put them to the sword
Kenny Dalglish's team were dominant and should have won the game, but did just enough to book their place at Wembley, where they will face Cardiff City, winning the tie 3-2 on aggregate.
Nigel de Jong had pulled City back into the tie by opening the scoring from distance, before Steven Gerrard's levelled the score with a penalty before half time.
Liverpool continued to press, but City goalkeeper Joe Hart was outstanding and Edin Dzeko tapped in with a goal that would have seen Roberto Mancini's team progress on away goals after extra time.
The game did not reach that stage, though, as the excellent Bellamy finally solved Hart to seal the tie.
Bellamy started alone up front for Liverpool, with Dirk Kuyt and Stewart Downing flanking a five-man midfield. Andy Carroll was forced to settle for a place on the bench.
Mancini chose to withdraw Sergio Aguero from his starting lineup, opting for a 3-4-2-1 formation that was perhaps designed to aid young defender Stefan Savic. Pablo Zabaleta and Aleksandar Kolarov filled wing-back roles, with Micah Richards shifting into the centre of defence alongside Savic and Joleon Lescott.
City struggled to gain a foothold in the game early on. The midfield trio of Gerrard, Jordan Henderson and Charlie Adam efficiently controlled possession, with the visitors' three centre-backs not containing the threat of the energetic Bellamy particularly successfully.
Hart superbly denied Jose Enrique from close range, with Downing blasting the rebound high and wide, before Adam tested the goalkeeper from distance.
Bellamy did beat Hart just prior to the 25 minute mark after sneaking in behind Savic and Lescott, but the Welshman was ruled offside.
The City threat through the first half hour was minimal, though, with only Silva finding the space to slide a pass just out of the reach of the surging Kolarov. The Serbian retrieved the ball in the penalty area but Daniel Agger did well to clear his cross aimed at the back post.
Silva was again involved as City took a surprise lead, cancelling out the Reds' first leg advantage. The Spaniard laid on a pass to de Jong, who brilliantly curled past Pepe Reina from 25 yards while losing his footing on the slippery Anfield surface.
While City began to counter-attack with more speed and confidence, the home side continued to press and dominate the ball. A superb Adam cross from the left was well cut out by Lescott, with Kuyt lurking.
Adam was again the creator as Liverpool grabbed a controversial equaliser. When the 26-year-old's low cross from the right bounced out to Agger, there was little Richards could do to prevent the shot hitting his arm. Referee Phil Dowd was unforgiving and pointed to the spot, with Gerrard coolly slotting home to restore his team's one-goal aggregate lead.
Liverpool had targeted the inexperienced Savic during the first half and Mancini relieved the Montenegrin centre-back of his duties at the break. Aguero was introduced, with City reverting to a more familiar 4-2-3-1.
A good Liverpool move down the right-hand side allowed Kuyt to sting Hart's palms with a driven effort that deflected off of Richards, before the 24-year-old 'keeper made a stunning save to deny Martin Skrtel, who had latched on to a loose ball in the City penalty area.
His heroics did not end there. Minutes later he flung himself in the way of Downing's volley after Kuyt had broken away down the right and crossed for the unmarked English winger. Pre-occupied with defending, City struggled to sustain any sort of attacking pressure.
Still, though, they found another goal. Kolarov charged down the left and fired in a wonderful cross that evaded Aguero but was met by Dzeko, who tapped in at the far post.
With their two shots on target, City had scored two goals and they had little grounds for complaint when Liverpool stepped back into the lead. After receiving a pass from Kuyt, Bellamy found enough space to shoot beyond Hart after an intricate one-two with Glen Johnson.
Substitute Adam Johnson tested Reina and Dzeko had a shot from close range blocked but Liverpool held out for the chance to take on the Bluebirds at Wembley.