Luke Moore came off the bench to score the winner in a dramatic victory over Manchester City at the Liberty.
In a match full of drama, Scott Sinclair had seen his penalty saved by Joe Hart after six minutes after the keeper had brought Wayne Routledge down in the box.
But it was the introduction of Moore that changed the match, with the striker heading home Routledge's cross with just six minutes left.
The drama didn't end there. The visitors soon had the ball in the net themselves via Micah Richards, only to see that effort chalked off for offside.
A tense four minutes of added on time followed, but the Swans hung on to add another famous victory over the big clubs with Arsenal already beaten at the Liberty.
This victory moved the Swans 14 points clear of the dropzone with ten games to go.
As expected, Brendan made just one change to the starting XI.
With Nathan Dyer serving the first of his three-match ban, Wayne Routledge came in on the right wing.
Other than that, it was the same XI that won at Wigan the previous weekend, though Leroy Lita returned to the bench after overcoming a virus.
The visitors named Stefan Savic as the man to replace the injured Vincent Kompany in the heart of defence following his injury in the Europa League defeat against Sporting Lisbon.
Roberto Mancini included Mario Balotelli and David Silva - a scorer in the opening-day clash at the Etihad Stadium - in his starting line-up while Sergio Aguero, Edin Dzeko and David Pizarro were among the substitutes.
Swans: Michel Vorm, Angel Rangel, Steven Caulker, Ashley Williams (capt), Neil Taylor, Leon Britton, Joe Allen, Gylfi Sigurdsson, Wayne Routledge (Garry Monk, 88), Scott Sinclair, Danny Graham (Luke Moore, 79).
Subs: Gerhard Tremmel, Alan Tate, Mark Gower, Josh McEachran, Leroy Lita
Manchester City: Joe Hart, Micah Richards, Gael Clichy, Stefan Savic, Kolo Toure (capt), Yaya Toure, Nigel De Jong (Adam Johnson, 84), Gareth Barry (Sergio Aguero, 38), David Silva (Edin Dzeko, 88), Samir Nasri, Mario Balotelli
Subs: Costel Pantilimon, Aleksander Kolarov, James Milner, David Pizarro
Referee: Lee Mason
On a sunny afternoon with an excellent playing surface, this was sure to be a thrilling game.
The Swans made a decent start, Wayne Routledge firing over with a volley after Neil Taylor's cross was half cleared.
Then, a great chance came the hosts' way with just six minutes on the clock. Scott Sinclair fed a through ball intended for Gylfi Sigurdsson but that failed to find the Icelandic midfielder. Routledge anticipated it and ran onto the loose inside the box before keeper Joe Hart arrived late and took down the winger.
Referee Lee Mason had no option other than to give the penalty, with Sinclair stepping up.
But Hart made up for his error, diving down low to his right to deny Sinclair - who had scored from his previous four penalties this season.
Nigel De Jong picked up the first yellow card in the 18th minute as, following great work by Danny Graham, the Swans set off on a counter attack which culminated with the Dutch midfielder bringing Routledge down on the halfway line with a challenge from behind.
The Swans were enjoying the majority of possession, with the visitors sitting back and looking to counter.
And they created another chance, Sigurdsson's curling cross finally finding Graham after Allen's neat touch, but the striker's shot bundled wide.
Angel Rangel then saw his shot stopped in its tracks by Kolo Toure after a cross had been half cleared.
Mancini had seen enough of his side being on the back foot, and he made a change after 38 minutes with Sergio Aguero replacing Gareth Barry in an attempt to pressurise the Swans back four.
City then went close themselves, Yaya Toure seeing his effort deflected over during a series of corners before David Silva fired just wide with a powerful drive.
Half-time: Swans 0 Man City 0
The Swans again started the half brightly, with Graham's tantalising low cross along the face of goal touched out for a corner by Micah Richards at the back post.
City replied with Samir Nasri seeing his effort saved comfortably by Vorm before the visitors were calling for a penalty after Balotelli went tumbling over in the box. Mason waved away the appeals, with replays showing Balotelli and Allen had collided outside the box.
Yaya Toure then tested Vorm's reflexes as the keeper had to react quickly to save low down as the visitors enjoyed a large period of pressure.
With 11 minutes left, Brendan made his first change with Luke Moore replacing Graham.
And it paid dividends. After Sigurdsson robbed possession in midfield off Savic, the ball worked its way to Routledge via Britton and Rangel. His cross found the unmarked Moore at the back post and he nodded into the far corner.
Then came the late charge.
Vorm denied Richards and then Yaya Toure with fine saves before both sides made changes for the remaining minutes.
Garry Monk replaced Routledge for the hosts with Edin Dzeko coming on for Silva.
City thought they had found an equaliser with Micah Richards heading past Vorm in the last minute of normal time, but referee assistant Sian Massey waved the flag for a clear offside.
The drama would continue in added on time, keeper Hart coming up for a series or corners.
But the Swans held on.
In a bizarre twist, they could have actually doubled their lead as, with Hart stranded in the Swans box following a corner, the hosts cleared with Sinclair racing down the right flank.
In almost the exact spot in which Darren Pratley had scored from to seal the Swans' Play-Off final spot last May, Sinclair went for goal only to see it stop just short and wide.
But that was that.
The Liberty erupted as the final whistle blew to seal another memorable victory - one that could prove vital in the survival race.