Glasgow will travel to Leinster for their RaboDirect PRO12 semi after beating Connacht 20-3 on Friday.
Warriors coach Gregor Townsend had made nine changes to his side that had already secured a play-off position. Hoping that results elsewhere would go their way, they had to win to have any chance of claiming home advantage in the semis.
It was an emotional night for Connacht's flanker Johnny O'Connor, in his last ever game before retiring from a 146 game career with the province, while coach Eric Elwood also ended his time at the Sportsground after the game.
Candian international DTH van der Merwe wrote his name into the Glasgow record books after 16 minutes, with his 25th try for the Scotstoun outfit. Ruaridh Jackson's conversion, added to his penalty minutes earlier, gave Glasgow a ten-point lead, which was reduced by three as Dan Parks slotted Connacht's first points a minute before the half-time whistle.
The visitors had to defend while being a man down for ten minutes after prop John Welsh was yellow carded halfway through the period, but Connacht couldn't make their numerical advantage pay.
Jackson missed an early second-half opportunity to stretch the lead, as the game entered a period where the hosts gained the upper hand, with Connacht turning the screw on Glasgow.
But Stuart Hogg, buoyed by his inclusion in the forthcoming Lions party, came off the bench to add a penalty after 66 minutes, before the best move of the match came just moments later, as his Lions colleague Sean Maitland crossed the line after evading the desperate lunge of Tiernan O'Halloran. Hogg's conversion from the touchline gave his side a 20-3 lead with ten minutes to play, a scoreline that remained until the final whistle.
Tries: Van der Merwe, Maitland
Con: Jackson, Hogg
Connacht: 15 Gavin Duffy (capt), 14 Danie Poolman, 13 Eoin Griffin, 12 Brian Murphy, 11 Fetu'u Vainikolo, 10 Dan Parks, 9 Kieran Marmion, 8 Eoin McKeon, 7 Johnny O'Connor, 6 Andrew Browne, 5 Mike McCarthy, 4 Michael Swift, 3 Ronan Loughney, 2 Ethienne Reynecke, 1 Brett Wilkinson.
Replacements: 16 Adrian Flavin, 17 Rodney Ah You, 18 JP Cooney, 19 Mick Kearney, 20 John Muldoon, 21 Mata Fifita, 22 Paul O'Donohoe, 23 Miah Nikora.
Glasgow: 15 Peter Murchie, 14 Tommy Seymour, 13 Sean Lamont, 12 Peter Horne, 11 DTH Van der Merwe, 10 Ruaridh Jackson, 9 Henry Pyrgos, 8 Ryan Wilson (c), 7 John Barclay, 6 Rob Harley, 5 Tom Ryder, 4 Tim Swinson, 3 Jon Welsh, 2 Pat MacArthur, 1 Moray Low.
Replacements: 16 Doug Hall, 17 Ryan Grant, 18 Ed Kalman, 19 James Eddie, 20 Josh Strauss, 21 Niko Matawalu, 22 Sean Maitland, 23 Stuart Hogg.
Referee: George Clancy (Ireland)
Assistant referees: Paul Haycock (Ireland), John Carvill (Ireland)
Television match official: Seamus Flannery (Ireland)
Citing Commissioner: John Cole (Ireland)