On a night when Premier League club West Bromwich Albion were dumped out by second tier Bournemouth, both Liverpool and Chelsea flirted with danger before reaching the quarter-finals.
Liverpool fans have seen precious little in Balotelli's performances this season to convince them he could ride to the rescue when the chips were down but he came off the bench to turn the clash with Swansea on its head.
Entering the fray on 79 minutes, the Italian took seven minutes to level the scores as he stole in front of his marker to prod home a cross from compatriot Fabio Borini after Marvin Emnes had put Swansea ahead midway through the second half with a superb volley.
A sustained roar erupted around Anfield as Balotelli's effort found the net, as much in celebration of the goal as it was grounded in relief that the misfiring striker had finally found his range at a crucial time.
It was the start of a dramatic finale that saw Swansea's Federico Fernandez sent off for a late tackle and Dejan Lovren head home the winner after four minutes of stoppage time, to leave eight-times winners Liverpool well-placed to launch another assault on a trophy they last won in 2012.
Premier League leaders Chelsea will also fancy their chances of getting their hands on a cup they have won four times but they needed a wake-up call before ousting fourth tier Shrewsbury 2-1.
"I wasn't expecting anything but a difficult match. I was ready for extra-time," Chelsea manager Jose Mourinho said, and he was not wrong.
Didier Drogba gave them the lead, with his third goal in three games, but the match seemed headed for extra-time when Shrewsbury's Andy Mangan swivelled to fire past keeper Petr Cech with 13 minutes to play.
Nemanja Matic and Willian were promptly summoned from the bench to help quell the uprising, the latter's superb cross causing panic in the defensive ranks and Jermaine Grandison turning the ball into his own net.
"I don't say relieved with the result. I am happy with my players' approach. You're playing a World Cup final because that is what it is for Shrewsbury," Mourinho added.
West Brom probably thought they had done enough to force extra-time when a Tommy Elphick own goal with five minutes to go at Bournemouth levelled the scores at 1-1.
But it was the hosts who progressed thanks to Callum Wilson's late strike, capping a superb few days for the south coast club after they thrashed Birmingham City 8-0 in the Championship at the weekend.
Bournemouth almost went bust in 2008 and only avoided relegation from the Football League on the last day of the following season having been docked 17 points for going into administration.
Elsewhere on Tuesday, Derby County came from 2-0 down to beat Championship rivals Fulham 5-2 and Sheffield United downed Milton Keynes Dons 2-1 in an all-League One encounter.
On Wednesday, holders Manchester City face Newcastle United while Tottenham Hotspur take on Brighton and Hove Albion and Stoke City host Southampton.

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