Glasgow upset London Wasps with a 20-10 victory Pool 6 of the Heineken Cup at Fir Hill on Sunday afternoon.
Wasps host Toulouse next weekend in the final round of matches and must hope that they beat their opponents, and other results go their way, so they can snatch one of the two best runners-up spots and a place in the quarter-finals.
The Scottish side scored 17 unanswered points after trailing 10-3 with just 11 minutes played at Firhill.
Colin Gregor crossed for his side's only try nine minutes into the second period, while Scotland fly-half Ruaridh Jackson finished with a personal tally of 15 points courtesy of a brace of penalties in either half and a late drop goal.
Tom Varndell was Wasps' solitary try scorer, with Dave Walder kicking five points from the tee as the visitors suffered their second defeat of the group stages.
Having starred in the reverse fixture in Wycombe back in October, scrum-half Joe Simpson was again the brightest spark of an otherwise disappointing Wasps display. Recently named in England's 33-man Six Nations squad, the 22-year-old was a constant threat with his sniping runs and sharp service.
It was his break that set up Varndell for the game's opening try. Simpson took possession at the back of a scrum on halfway before speeding through a gaping hole in the Glasgow defence. Having forced the Warriors' defensive cover to come inside in order to hault his own run, Simpson then threw a beautifully weighted long pass out to Varndell on the left wing.
Walder added the extras after he and opposite number Jackson had shared earlier penalties.
Jackson slotted a second successful strike with just a quarter of an hour played but Wasps held their 10-6 advantage until the half-time break.
Glasgow narrowed the gap to just a single point courtesy of Jackson's third penalty four minutes into the second period and the hosts found themselves ahead for the first time when Gregor crossed for a superb score five minutes later.
Colin Shaw's wonderful weaving run and deft offload gave his No9 an easy run in and sent an exuberant Firhill faithful absolutely wild.
Jackson failed with the relatively straightforward conversion and again with a 64th-minute penalty but he made amends 30 seconds later with his third successful three pointer.
The young playmaker then added a drop goal with five minutes remaining to deny Wasps a losing bonus point and hand Pool 6 to reigning champions Toulouse.
Final Score Glasgow 20 (10) Wasps (6) 10
Penalties: Jackson 4
Referee: James Jones (Wales)
Glasgow Warriors: B Stortoni, C Shaw, F Aramburu, P Murchie, H O'Hare, R Jackson, C Gregor, R Grant, D Hall, M Low, R Gray, A Kellock [capt], R Harley, R Vernon, R Wilson.
Replacements: P MacArthur, K Tkachuk, J Welsh, A Muldowney, C Fusaro, H Pyrgos, P Horne, D McCall
London Wasps: M van Gisbergen, T Varndell, B Jacobs, R Flutey, D Lemi, D Walder, J Simpson, T Payne, T Lindsay, Z Taulafo, S Shaw, J Cannon, J Worsley, S Betsen, A Powell