In an enthralling contest that belied the dreadful conditions, the Magpies overcome the loss of Brent Macaffer (knee), Dane Swan and Clinton Young (both hamstring) to seal a 11.9 (75) to 9.13 (67) triumph.
Vote for your top three players from Collingwood's gutsy eight-point win in the Magpie Army Player of the Year Award.
The result lifts the Pies into eighth place ahead of next week's clash with Hawthorn, although Richmond will replace them if it gets past St Kilda at the MCG on Sunday.
In front of 10,851 fans, the Giants' second biggest Spotless Stadium crowd this year, Josh Thomas' goal with less than six minutes remaining in the match remarkably gave the Pies the lead for the first time all game.
Steele Sidebottom then added a late sealer as Collingwood kicked the final three goals of the match to steal the critical four points.
With only one rotation on the bench from early in the third term, the victory would have to rate among the Pies' best in recent memory.
Defeat was still cruel on the Giants, however, who led by as much as 21 points in the second term and were desperately unlucky to end up on the losing end of such a quality contest.
GWS also had injury troubles of its own, with Phil Davis (calf) a late withdrawal, adding his name to fellow co-captain Callan Ward, Tom Scully, Jeremy Cameron, Lachie Whitfield and Jon Patton among the Giants' casualty ward.
In the end the Pies' cool heads prevailed in the dying moments, led by the exceptional Thomas (29 touches, three goals).
He was backed up by Scott Pendlebury (28 touches, nine clearances), Marley Williams (20 touches, seven inside 50s) and Tim Broomhead (23 touches, two goals) for the visitors.
Toby Greene was brilliant for the Giants, picking up 27 touches to half-time and finishing with a career-best 42, also adding one goal and six inside 50s to his day's work.
Devon Smith (23 touches, two goals), Josh Kelly (28 touches, six tackles) and Shane Mumford (46 hitouts, nine tackles) were all brilliant for the home side, which fell agonisingly short of its sixth win of a vastly improved 2014.
The Giants were up for the contest from the first bounce, quickly registering the game's first three goals to establish an early 20-point lead.
Collingwood finally kicked into gear late in the term, with Broomhead and Jesse White kicking majors to make it just a seven-point GWS lead at quarter-time.
The second term then followed a similar script, with the Giants again dominating possession and kicking three more goals before the Pies responded once more.
Broomhead and White were again prominent in the comeback, with Jarryd Blair's clever late effort off the ground from the goalsquare dragging the Pies back within seven points at half-time.
The match was an absolute arm-wrestle from that point on, with both sides kicking two goals apiece in the third term as GWS enjoyed a 10-point edge heading into the final quarter.
But four goals to one in the final quarter allowed Collingwood to seal a famous victory that keeps its season alive.
Collingwood 2.3 5.5 7.7 11.9 (75)
Greater Western Sydney 3.4 6.6 8.11 9.13 (67)
Goals - Collingwood: Thomas 3, White 2, Broomhead 2, Williams, Blair, Sinclair, Sidebottom
Greater Western Sydney: Smith 2, Boyd, Hunt, Palmer, Whiley, Bugg, Greene, Hoskin-Elliott
Best - Collingwood: Thomas, Pendlebury, Broomhead, Williams, Armstrong, White
Greater Western Sydney: Greene, Mumford, Smith, Kelly, Shiel, Hunt
Injuries - Collingwood: Young (hamstring), Swan (hamstring), Macaffer (knee)
Greater Western Sydney: Davis (calf) replaced in the selected side by Frost, O'Rourke (hamstring)
Substitutes - Collingwood: Clinton Young replaced by Luke Ball in the second quarter
Greater Western Sydney: Jono O'Rourke replaced by Tim Golds in the first quarter
Reports: Nil
Umpires: Donlon, Fisher, Hosking
