Meanwhile Cardiff of the Championship had a comfortable 2-0 victory over Blackburn, bottom of the Premier League.
Andy Carroll had his 22nd minute penalty saved but Liverpool scored two after the break to save the striker’s blushes.
Craig Bellamy was provider for both the Reds strikes in a quickfire five minute spell just after the break.
The last time Arsenal had lost as home in the League cup was 2004 and for City they hadn’t won against their host’s on home soil for 36 years.
Park Chu-young and Alex Oxlade-Chamberlain tested City's goal in the first half but it is Roberto Mancini’s men who progress into the last four.
Cardiff City reached the League Cup semi-finals for the first time since 1966 in what was hardly a giant-killing act against Blackburn who are having a woeful season in the top flight.
Rovers were looking to make the semi-finals for the fourth time since lifting the trophy in 2002, and the seventh in their history, but once Kenny Millar opened the scoring with a neat finish midway through the first-half the result never looked in doubt.
The Premiership outfit rarely troubled the Bluebirds and the game was made safe soon after the break when Filip Kiss doubled the South Wales side advantage.
Poignant scenes preceded the match as respect was paid to Wales coach Gary Speed, whose body was found on Sunday.