A 2-2 draw was enough for Kenny Dalglish's side to book their place alongside Cardiff City in the Wembley final.
The hosts almost took the lead as early as the third minute, but Joe Hart was able to save Jose Enrique's close-range effort. Stewart Downing was on hand for the rebound, but the winger smashed the ball high and wide.
Hart came to City's rescue again on 20 minutes when he parried Craig Bellamy's stinging effort.
However, Liverpool continued to control proceedings after the goal and were rewarded for their efforts five minutes before half time when referee Phil Dowd gave a penalty for Micah Richards's contentious handball. Steven Gerrard stepped up to fire past Hart.
The Reds nearly went ahead soon after the restart, but Hart was again able to deny them as Martin Skrtl's poked shot was turned over the bar.
However, their lead only lasted five minutes as former City striker Bellamy fired past Hart following an exchange of passes with Glen Johnson.
Adam Johnson came close for the visitors with ten minutes to play, but his left-footed curler flew wide.
As City pushed for the winner, Dzeko nearly bagged his second, but his shot was blocked by a frantic Liverpool defence.