Mario Balotelli had given City a first-half lead before Gareth Barry put through his own net on the hour to level the scores.
Aleks Kolarov scored a trademark free-kick to restore the Blues’ lead four minutes later, but Vila again equalised through Gabriel Agbonlahor shortly after to send the game into extra time where Villa scored twice more to send Paul Lambert’s men into the last 16 of the competition.
City’s wait for League Cup glory will now extend to at least a 38th year.
Roberto Mancini elected to give Spanish teenager Denis Suarez his full senior debut as he changed his entire starting XI from the team that began against Arsenal on Sunday.
Abdul Razak was starting only his third game while Kolo Toure was handed the captain’s armband for the visit of Paul Lambert’s side.
With an unfamiliar back three of Matija Nastasic, Toure and Joleon Lescott - the latter replacing Jack Rodwell who was injured in the warm-up - it was a case of getting-to-know-you for the majority of the team in the early stages and much of the first-half.
Despite the wholesale changes in personnel, City still fielded a team that would more than hold its own in the Premier League while Villa, a mixture of experience and youth, made five changes from the team that lost 3-1 to Southampton at the weekend.
The incessant Manchester rain was partly to blame for the crowd of 28,015, but the early rounds of the League Cup have always struggled to attract decent numbers for several years now
...City 2 Villa 4...
Still, it was a respectable number considering the appalling weather.
Villa, who had lost on their last six successive visits to the Etihad Stadium, began brightly and N’Zogbia was a whisker away from connecting with Fabian Delph’s low cross on ten minutes with Costel Pantilimon stranded.
With neither team able to fashion much in the way of free-flowing football or retain possession for any length of time, the game was crying out for a goal – and on 27 minutes, City finally lifted the gloom with the opening goal.
James Milner collected the ball on the right of the box, cut back inside and found Balotelli on the penalty spot where the Italian controlled the ball before slotting past Shay Given for his sixth goal against Villa in just four appearances – clearly a team he enjoys playing against!
Two goals in the space five minutes after the break livened proceedings further with more than a touch of irony about Villa’s equaliser.
Joe Bennett found himself in space on the right and drilled in a low cross that evaded everyone except former Villa skipper Barry who watched helplessly as the ball struck him and went onto his own net.
City, however, were back in front on 64 minutes when Balotelli won a free-kick 25-yards out and Kolarov curled yet another a beauty past Given to make it 2-1.
In what was becoming a fascinating contest, Villa again fought their way back into the tie but the manner in which Agbonlahor waltzed through the midfield and centre of City’s defence to plant the ball home and make it 2-2 on 70 minutes will have infuriated Mancini.
Both teams had chances to win in normal time with City going close through a Balotelli header and Tevez hit the bar with a free-kick in the last minute before the match went into extra time.
But it was the visitors who went on to score twice more - once in each half - with N’Zogbia tapping home on 96 minutes and Agbonlahor scoring his second after 113 minutes to send City crashing out.
