Sydney has inflicted another heartbreaking loss on Richmond, winning a thriller by nine points after the Tigers had led by 36 points early in the second quarter.
The Swans kicked eight of the last nine goals, with midfielder Kieren Jack's banana goal putting them in front late in the final quarter for the first time since the opening minutes of the game.
After a pulsating final five minutes, Gary Rohan kicked the sealer with less than a minute to go to seal the 12.8 (80) to 10.11 (71) win.
The win puts the Swans back in the finals hunt, just one game out of the eight, and once again raises doubts about Richmond's ability to close out games.
However, the Swans' win could come at a cost with superstar forward Lance Franklin reported for a high bump on Richmond's Connor Menadue in the second quarter.
It was an enormous effort from the Swans, who regained their composure after a shocking first quarter when the Tigers kicked five goals to zero.
It was the first time Sydney had been kept goalless in the first quarter since round 17, 2015.
The Tigers' dominance had been sparked by fourth-gamer Shai Bolton, who kicked two goals and had seven contested possessions at quarter-time to be the dominant player on the ground.
The Swans squared the contest in the second quarter and, helped by a late goal caused by a turnover from Tiger forward Sam Lloyd, managed to keep the margin to just 25 points.
They then dominated territory in the second half, recording 30 inside 50s to Richmond's 20 as the Swans' midfield went to work, winning contested possession 90 to 71.
Sydney Swans coach John Longmire praised his team's effort to dig themselves out of the hole.
"It was a bit of a concern getting six goals down but to our players' credit, they just kept persisting," Longmire said.
"There was blokes that weren't playing very well at the start that really turned their games around and really contributed."
Dan Hannebery was outstanding with 16 second-half possessions, and skipper Josh Kennedy lifted with an immense final quarter.
In a thrilling final term, the Tigers looked to be doing enough to hang on with Alex Rance brilliant in defence, his enthralling battle with Franklin living up to the pre-game hype.
The Tigers managed a goal - their only major of the final term - against the run of play after a controversial free kick for a centre-square infringement.
But Rance could not save the game alone and when Rohan intercepted a Shaun Grigg kick gifting Sydney's Sam Reid a goal, the momentum was with the Swans.
Their midfielders were relentless in getting numbers to the ball and eventually overwhelmed Richmond.
Tigers coach Damien Hardwick was disappointed they gave up such a good lead, bemoaning missed set shots in the last quarter and the Tigers' inability to cash in on momentum.
Yet it was their inability to defend late in the game that Hardwick said was most costly.
"We had a really strong focus on controlling their scores from stoppages, a strength of theirs, and they kicked four [goals from stoppages] in the last quarter," Hardwick said.
"We just couldn't get that part of our game right, which is disappointing."
NEXT UP
Richmond has an eight-day break before playing Carlton in a blockbuster at the MCG, while Sydney returns home to play Essendon on Friday night. The Swans may be without Franklin who has kicked 64 goals and averaged 4.92 goals a game against the Bombers.
MEDICAL ROOM
Richmond: Dylan Grimes injured his ankle in the last quarter and had to be re-strapped. He will be assessed.
Sydney Swans: Tom Papley appeared to cramp in the third quarter and left the ground to recover.
RICHMOND 5.3 7.6 9.7 10.11 (71)
SYDNEY 0.4 3.5 7.6 12.8 (80)
GOALS
Richmond: Riewoldt 2, Martin 2, Bolton 2, Cotchin, Castagna, Edwards, Lloyd
Sydney: Reid 2, Franklin, Hewett, Lloyd, Heeney, Parker, Hayward, Papley, Kennedy, K.Jack, Rohan
BEST
Richmond: Rance, Houli, Cotchin, B.Ellis, Astbury, Martin
Sydney: Lloyd, Newman, Heeney, Jones, Mills, Hannebery, Reid
INJURIES
Richmond: Grimes (lower leg)
Sydney: Nil
Reports: Franklin (Sydney) for rough conduct on Menadue (Richmond) in the second quarter.
Umpires: O'Gorman, Nicholls, Williamson
Official crowd: 58,721 at the MCG
