The Lions trailed by 52 points late in the third term, and kicked 10 of the last 11 goals to win 15.13 (103) to 14.14 (98) in the equal eighth-biggest comeback in VFL/AFL history.
In his 200th career game, McGrath took a mark on the 50m arc with just seconds remaining.
The 30-year-old then coolly went back and slotted the winner after the siren.
The Lions looked shot on a number of occasions, but with huge final quarters from Brent Moloney (11 disposals) and new club games record-holder Simon Black (12), they completed the remarkable turnaround.
The trailed by 38 points at the last change and kicked eight goals to one to send a raucous Gabba crowd of 24,164 into raptures.
Daniel Rich levelled the scores inside the final two minutes with a goal from 50m, only for Tom Hawkins to regain the lead for the Cats with a behind with a minute remaining.
The Lions then swept the ball forward desperately to McGrath, who marked just in time.
The win moves the Lions to a 4-8 win-loss record, while the loss was Geelong's second of the season. It came from nowhere.
It may come at further cost with Steve Johnson likely to come under scrutiny from the Match Review Panel for his first-quarter bump on Pearce Hanley.
The bump appeared to collect Hanley high and left the Irishman dazed and on the ground for a few moments.
The Cats looked in control for most of the day and extended their lead through each of the first three quarters with a combination of intensity and precision.
However, the match was turned on its head early in the fourth quarter with an amazing incident.
Johnson scrubbed a clearing kick into the feet of umpire Stuart Wenn, only for it to bounce back into the waiting hands of Daniel Rich, who fed Dayne Zorko for a running goal from 50m.
From there it was one-way traffic as the Lions stormed to an incredible win.
BRISBANE LIONS 3.2 5.4 7.8 15.13 (103)
GEELONG 5.3 9.7 13.10 14.14 (98)
GOALS
Brisbane Lions: McGrath 3, Moloney 3, Rich 2, Lisle, Patfull, Brown, Zorko, Adcock, Hanley, Golby
Geelong: Hawkins 3, Christensen 2, Motlop 2, Johnson 2, Mackie, Guthrie, Murdoch, Blicavs, Podsiadly
BEST
Brisbane Lions: Moloney, McGrath, Rich, Black, Redden
Geelong: Bartel, Johnson, Blicavs, Selwood, Stokes, Enright
INJURIES
Brisbane Lions: Nil
Geelong: Nil
SUBSTITUTES
Brisbane Lions: Ryan Harwood replaced Sam Mayes during the third quarter.
Collingwood: Jesse Stringer replaced Jordan Murdoch during the third quarter.
Reports: Nil
Umpires: Donlon, Bannister and Wenn
Crowd: 24,164
