The Swans came into the game with six losses from their past eight games, but overcame a 10-point half-time deficit and poor goalkicking to prevail 10.23 (83) to 10.8 (68).
The win puts the Swans into seventh and still within reach of a home final, while the sixth-placed Saints have lost their second straight game and are now only percentage ahead of the Swans.
Shane Mumford, Dan Hannebery, Josh Kennedy and Rhyce Shaw were outstanding for the home side, while Ted Richards kept Nick Riewoldt to two goals.
For the Saints, Sean Dempster and David Armitage played their parts, but the visitors were unable to withstand the Swans' intensity over the four quarters.
The match got off to a cagey start, with the Swans kicking the opening goal through Shaw before the Saints registered the next three to build an early advantage.
The Swans pressed late in the term, but as has been their problem all season, failed to convert their opportunities and entered the first break trailing 3.3 (21) to 1.5 (11).
The Swans' ineptitude in front of goal continued in the second term, with Adam Goodes and Jude Bolton hitting the post before the latter was denied a goal by an incorrect call from the umpires.
It was wrongly determined Bolton's goal was touched off the boot, with the Saints immediately kicking a goal through Stephen Milne to extend their lead to 13 points.
A run of 10 straight behinds was finally ended when a Ryan O'Keefe snap gave the Swans just their second goal of the game 17 minutes into the second quarter.
A late Jarrad McVeigh goal then reduced St Kilda's lead to 10 points at the main break.
The Swans finally discovered their accuracy in the third term, kicking three goals to take the lead for the first time since midway through the opening quarter.
The home side had all the momentum before the Saints answered, with Tom Lynch and Armitage kicking goals as they took a seven-point edge into the last change.
However, the final term was all the home side, who claimed a morale-boosting win with two games left before the finals.
Stats that matter
The Swans pumped the ball inside 50m a massive 39 times in the first half. But they could only manage three goals and 12 frustrating behinds. Alternatively, the Saints had 28 entries to their forward 50m to half-time, resulting in 6.4 and a 10-point half-time lead. But by the end of the match the Swans had enough reward for their dominance, winning the inside 50 count 68-52. Thanks to ruckman Shane Mumford, the Swans also destroyed St Kilda in the hit-outs 62-32.
Key match-up
Ted Richards spent most of the game on Nick Riewoldt and it was a battle the Swan won comfortably. Riewoldt kicked two first-half goals, one from a free kick and another from out-marking Richards. But Richards had plenty of impressive moments, including smothering an attempted Adam Schneider pass to Riewoldt to stop what appeared a certain goal. An exhausted, hurting Riewoldt had a shot late to keep his side in the game, but missed everything from a slight angle.
What the coach said
John Longmire (Sydney Swans): "There wasn't any point in getting too frustrated about it, in terms of talking to the players, even though it would've been better if we'd kicked straight. But the important thing from my point of view was just our intensity. That's what we brought and when we started to kick straighter obviously we were able to pull away."
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Sydney Swans: Big man Shane Mumford had a massive 54 hit-outs alongside 16 disposals to finish as his team's best with 146 points. He even iced the game with a goal in the last two minutes of the match.
QUARTER BY QUARTER
FIRST QUARTER
The players struggled to hold their feet and change direction with ease in the opening term with slippery conditions not helped by a burst of rain just before the bounce. But clouds soon gave way to sunshine and St Kilda made the best of the conditions, booting the last three goals of the quarter after Rhyce Shaw kicked the first for the home side.
SECOND QUARTER
St Kilda extended its advantage to 17 points midway through the term, absorbing the Swans' attacking moves and hitting the home side on the break. The Swans kicked the opening goal in the third minute, but had to wait 45 minutes to add another when Ryan O'Keefe crumbed and snapped truly from a marking contest in the 17th minute of the second term. In between, the team scored 10 behinds, including three posters. A goal to Jarrad McVeigh ensured the margin remained 10 points at the main interval.
THIRD QUARTER
The home side got the perfect start to the last half when Daniel Hannebery capitalised on some good lead-up play to run into an open goal from 30m after the Swans had taken the footy the length of the field. And when Sam Reid marked and goaled from 30m out in the 15th minute, they were in the lead for the first time since just before time-on in the opening term. But a turnover, and a free kick gifted St Kilda two goals before the last change kept the visitors' noses in front heading into the final term.
FOURTH QUARTER
A brilliant last-quarter rally helped the Swans turn around a seven-point three-quarter time deficit and secure four crucial premiership points. A three-goal burst in the opening five minutes of the term put the Swans in front and that's where they would stay as St Kilda managed just one goal. Saints skipper Nick Riewoldt, who spent time off the ground in the third term after teammate Jarryn Geary collided into his legs and Swan Shane Mumford leapt onto his back for a spectacular mark in the third term, tried to lift his team but looked bruised and battered. Riewoldt had two chances to score in the last term, but missed one and sprayed the other out on the full. He finished the match on the bench.
The run home
Sydney Swans: The Swans' final road trip of the home and away season next week is to the most daunting of venues - Skilled Stadium - for a Saturday afternoon clash against Geelong. In the final round, the team hosts the Brisbane Lions at the SCG.
MATCH DETAILS
Sydney Swans 1.5 3.12 6.17 10.23 (83)
St Kilda 3.3 6.4 9.6 10.8 (68)
GOALS
Sydney Swans: Shaw, McVeigh, Hannebery, O'Keefe, White, Reid, Bolton, Spangher, Goodes, Mumford.
St Kilda: Riewoldt, Armitage 2, Goddard, Gilbert, Ray, Lynch, Milne, Polo
BEST
Sydney Swans: Richards, Shaw, Mumford, Goodes, Hannebery, McVeigh
St Kilda: Dempster, Fisher, Dal Santo, Goddard, Armitage
INJURIES
Sydney Swans: Johnson (foot)
St Kilda: Dempster (head), Blake (leg). Koschitzke (gastro) and Dawson (gastro), replaced in the selected side by Baker and Lynch.
Reports: Dean Polo (St Kilda) reported in the last quarter for tripping Sydney Swans player Adam Goodes
SUBSTITUTES
Sydney Swans: Alex Johnson replaced by Gary Rohan in the third quarter
St Kilda: Tom Lynch replaced by Steven Baker at the start of the fourth quarter
Reports: Nil
Umpires: Farmer, Chamberlain, Ryan
Official crowd: 25,025 at ANZ Stadium, Sydney.
The views in this article are those of the author and not necessarily those of the AFL or its clubs
