Sydney survived a spirited challenge from Richmond and a controversial free kick after the siren to cement their place in the top eight with a six-point triumph at the SCG.
The Swans overran the Tigers with 10 goals to three in a second-half surge after trailing by as much as 33 points to prevail 16.10 (106) to 15.10 (100) on Friday night.
Dion Prestia had a shot after the siren that could have levelled the scores after Chad Warner was penalised for deliberately carrying the ball over the boundary line with a second remaining, but the Tigers midfielder was too far out to be a realistic chance to score.
Lance Franklin led the Swans' comeback to finish with five goals after being well held by Josh Gibcus in the first half, but will be sweating on the Match Review Officer's verdict of a high hit on Trent Cotchin.
Franklin received the Goodes-O'Loughlin Medal as best afield in the annual Marn Grook match at the SCG, the second time he has won the award, while Warner (27 disposals) continued his outstanding form and Luke Parker (26) was also influential.
Co-captain Callum Mills (20) was a key to the second-half turnaround as a loose player defence after the Swans leaked 11 goals to half-time despite leading the inside 50 count 32-22.
The Tigers resembled their premiership-winning best early on as they played with frenetic intensity and kicked seven unanswered goals either side of quarter-time.
Jayden Short (22 disposals, two goals) and Dion Prestia (24, one) led the way for the Tigers while Cotchin (25 touches) was inspirational throughout.
Dustin Martin (20) was important in the first three quarters but had little impact when the match was on the line in the final term.
The Swans will be waiting on the MRO verdict of a clash between Franklin and Cotchin in the second term.
Tempers flared as the pair came together while the Swans were lining up for a set shot on goal, Cotchin bumping into Franklin several times until the superstar forward lashed out with his right hand.
Cotchin clutched at his chin after the second swing from Franklin while the umpire awarded the Tigers' former skipper a free kick for high contact.
It was a frustrating first half for Franklin as he was well held by Gibcus, playing just his ninth match. The 19-year-old restricted his more experienced opponent to three disposals and a goal before Franklin came to life after the main break to lead the Swans to a rousing victory.
Sydney face reigning premiers Melbourne at the MCG next Saturday night while Richmond have the week off with a bye.