Match ends, Liverpool 2, Swansea City 1.
Mario Balotelli inspired a stirring comeback as Liverpool scored twice in the final few minutes to beat Swansea and reach the League Cup last eight.
The visitors led when Marvin Emnes hooked across Reds understudy keeper Brad Jones into the far corner.
Liverpool rarely threatened until substitute Balotelli guided in Fabio Borini's cross.
Swans defender Federico Fernandez was sent off before centre-back Dejan Lovren headed in the late winner.
Liverpool have made an indifferent start to the Premier League season as they look to replicate last year's second-place finish without the departed Luis Suarez.
Swansea, who are a place above their opponents in the top flight, looked set to eliminate the eight-time winners from the League Cup for the second time in three seasons with Emnes' opener.
Ex-Swans boss Brendan Rodgers watched his current team fall into a familiar pattern of dominating possession without finding a cutting edge.
That was until Balotelli, moved to the bench as one of nine changes to the Reds team which started Saturday's 0-0 Premier League draw against Hull, was introduced with little over 10 minutes left.
The Italy striker has faced heavy criticism for both his attitude and goalscoring record since arriving from AC Milan in August.
But he responded with a cameo performance that brought the Anfield crowd to its feet. His sharp movement led to the equalising goal and, after Fernandez was shown a straight red card for a lunge on Philippe Coutinho, he also unsettled the Swansea defence in the build-up to the winner.
Lovren, whose performances have also been questioned since his £20m move from Southampton, sparked wild celebrations in front of the Kop when he met Coutinho's free-kick to keep alive Rodgers' hopes of winning his first major silverware.
Liverpool assistant manager Colin Pascoe:
"With the way we were playing I thought we were always going to create a chance.
"I thought we were unfortunate to be 1-0 down as the way we played was possibly the best we've played all season, with the character of the lads to keep going and get the win.
"It's a win - even if it was so late. It's a great feeling."
Swansea City manager Garry Monk:
"I'm disappointed. It wasn't a red card, but these things are happening, and hopefully they will stop happening.
"With a couple of minutes to go, we should have seen it out. We should have defended better and come away with the win.
"But we put on a performance, especially the second half, that we can be proud of."
- 4K TouréBooked at 90mins
- 50MarkovicSubstituted forLallanaat 70'minutes
- 9LambertSubstituted forBalotelliat 79'minutes
- 33FernándezBooked at 90mins
- 6WilliamsBooked at 82mins
- 3TaylorBooked at 63mins
- 56FultonBooked at 51minsSubstituted forCarrollat 88'minutes
- 12DyerSubstituted forRoutledgeat 67'minutes
- 18GomisSubstituted forBonyat 82'minutes
- Keith Stroud
- Shots on Target
Second Half ends, Liverpool 2, Swansea City 1.
Corner, Liverpool. Conceded by Ashley Williams.
Attempt blocked. Philippe Coutinho (Liverpool) right footed shot from the centre of the box is blocked. Assisted by Bradley Jones.
Goal! Liverpool 2, Swansea City 1. Dejan Lovren (Liverpool) header from the centre of the box to the top right corner. Assisted by Philippe Coutinho with a cross following a set piece situation.
Adam Lallana (Liverpool) wins a free kick on the left wing.
Foul by Wayne Routledge (Swansea City).
Attempt blocked. Philippe Coutinho (Liverpool) right footed shot from outside the box is blocked. Assisted by Mario Balotelli with a headed pass.
Attempt missed. Mario Balotelli (Liverpool) right footed shot from outside the box is too high from a direct free kick.
Federico Fernández (Swansea City) is shown the red card.
Philippe Coutinho (Liverpool) wins a free kick in the attacking half.
Foul by Federico Fernández (Swansea City).
Attempt missed. Mario Balotelli (Liverpool) right footed shot from outside the box is too high. Assisted by Philippe Coutinho.
Kolo Touré (Liverpool) is shown the yellow card for a bad foul.
Foul by Kolo Touré (Liverpool).
Neil Taylor (Swansea City) wins a free kick in the defensive half.
Substitution, Swansea City. Tom Carroll replaces Jay Fulton.
Goal! Liverpool 1, Swansea City 1. Mario Balotelli (Liverpool) left footed shot from the centre of the box to the bottom right corner. Assisted by Fabio Borini with a cross.
Attempt missed. Jordan Henderson (Liverpool) right footed shot from outside the box is high and wide to the right. Assisted by Fabio Borini.
Foul by Javier Manquillo (Liverpool).