Balotelli has struggled since his £16 million pre-season move from AC Milan and on Tuesday he was on the bench until 11 minutes from time.
When the Italian striker was sent on by Reds boss Brendan Rodgers – a former Swansea manager – Liverpool were trailing 1-0 to Marvin Emnes's 65th-minute goal.
But four minutes from time, Balotelli evaded the visitors' defence to equalise. Then, with extra-time looming, Swansea's Federico Fernandez was controversially sent off for a challenge on Philippe Coutinho.
And, with Liverpool now at an advantage, the fifth minute of stoppage-time saw Liverpool's Dejan Lovren get on the end of a Coutinho free-kick, that Swansea keeper Gerhard Tremmel came for and missed, to head home the winner — his first goal for Liverpool.
Balotelli posted a one-word tweet of ‘finally’ to express his relief at scoring, while Liverpool assistant manager Colin Pascoe said, "He is working hard in training and he got his just rewards coming on and getting the goal."
Meanwhile, Swansea manager Garry Monk said he hoped referee Keith Stroud would overturn Fernandez's red card.
Mourinho unimpressed by understudies
Chelsea manager Jose Mourinho said that some of his squad players had made his team selection ‘easy’ after they struggled to overcome fourth-tier Shrewsbury Town in the League Cup.
Chelsea booked their place in the quarter-finals with a 2-1 win on Tuesday, but it took an 81st-minute own goal by Jermaine Grandison to send them through after Andy Mangan cancelled out Didier Drogba's opener.
Andre Schuerrle, Mohamed Salah and Filipe Luis were among the fringe players given opportunities to shine and Mourinho, who made seven changes to his starting XI, said they had failed to impress.
"I expect players to give me problems. I love problems. But a lot of them didn't and they've made it easy to choose my team for Saturday," said Mourinho, whose side host Queens Park Rangers this weekend.
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Balotelli would have performed from day one if Rodgers wouldn't have isolated him as a lone striker.