Victory at the Sportsground on Friday, with other results also going their way, would allow Warriors to achieve their aim.
Head coach Gregor Townsend said: "We were delighted with our performance against the Ospreys which secured our play-off spot, but we know we'll face a big challenge tomorrow night at a ground we've not won at since 2007."
He added: "Connacht are enjoying a great run of form at the moment, having lost just twice in their last seven games, so it will be an extremely tough game for us, but one we're all looking forward to."
Townsend has made nine personnel changes to the team that beat the Ospreys 35-17 at Scotstoun last month, for the final game of the regular season.
There are also two positional switches from the team that secured their play-off place against the defending champions, with only Sean Lamont, Pat MacArthur, Moray Low, Tim Swinson, Rob Harley and John Barclay remaining in the starting XV.
British and Irish Lions pair Stuart Hogg and Sean Maitland drop to the bench, along with Niko Matawalu, Ryan Grant and Josh Strauss. Alex Dunbar, Graeme Morrison, Duncan Weir and Al Kellock drop out of the squad altogether for the trip to Galway.
Peter Murchie comes in at full-back in place of Hogg, Tommy Seymour replaces Maitland on the right wing and DTH van der Merwe comes in on the opposite side, with Lamont moving to outside centre in place of Dunbar.
Peter Horne replaces Morrison at inside centre, Ruaridh Jackson comes in for the injured Weir at fly-half and Henry Pyrgos replaces Matawalu at scrum-half. In the pack, Low moves from tighthead to loosehead in place of Grant, with Jon Welsh coming in at tighthead and MacArthur continuing at hooker.
Club captain Kellock drops out of the squad for the trip to Ireland as his wife has just given birth, so Swinson and Tom Ryder combine in the second row. Ryan Wilson is given the captaincy and comes in at number eight, with Harley continuing at blindside and Barclay keeping his place at openside.
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- Sean Lamont