Tries from Sean Maitland and Sean Lamont guided Glasgow to a notable 15-10 away win over Exeter Chiefs at Sandy Park.
Exeter's Heineken Cup hopes ended thanks to a solid Glasgow performance. The Chiefs were unable continue a bright early start which saw them 10 points up.
Exeter were straight out of the blocks, taking a 3-0 lead after two minutes thanks to Henry Slade, who has been taking over kicking duties in the absence of Gareth Steenson.
After the Chiefs had scored the early points, the game struggled to get going. Handling errors and indiscipline disrupted the game until the hosts managed to score the first try of the match.
Fetu'u Vainikolo burst over the line from short range under the posts, and despite waiting for the TMO to confirm, Rob Baxter's men had the score that their bright start had deserved.
Lamont then took matters into his own hands. First, Glasgow stretched the host's line and found the Scottish international in the corner. Then, with five minutes until half time, a move which spanned 60 metres was finally finished by Lamont, with Stuart Hogg's superb conversion sending the visitors in with a 12-10 lead.
Glasgow, who have impressed in the Pro 12 league this season and sit in fifth place, were the brighter of the two teams after the break, with Hogg slotting his first penalty of the game to extend the Scottish side's lead to five.
On the hour mark, Slade missed the chance to get the Chiefs back on the coattails of the Warriors, skewing wide a long distance attempt.
That, as it turned out, was the last real chance of the game which confirmed that both teams will bow out of the Heineken Cup with a game to go.
Tries: Maitland, Lamont
Exeter Chiefs: 15 Luke Arscott (capt), 14 Fetu'u Vainikolo, 13 Sireli Naqelevuki, 12 Sam Hill, 11 Matt Jess, 10 Henry Slade, 9 Dave Lewis, 8 Kai Horstmann, 7 James Scaysbrook, 6 Tom Johnson, 5 James Hanks, 4 Damian Welch, 3 Alex Brown, 2 Luke Cowan-Dickie, 1 Carl Rimmer.
Replacements: 16 Greg Bateman, 17 Ben Moon, 18 Lloyd Fairbrother, 19 Romana Graham, 20 Don Armand, 21 Will Chudley, 22 Ceri Sweeney, 23 Ian Whitten.
Glasgow Warriors: 15 Stuart Hogg, 14 Sean Maitland, 13 Byron McGuigan, 12 Alex Dunbar, 11 Sean Lamont, 10 Ruaridh Jackson, 9 Henry Pyrgos, 8 Josh Strauss, 7 Chris Fusaro (capt), 6 Rob Harley, 5 Tom Ryder, 4 Tim Swinson, 3 Ed Kalman, 2 Dougie Hall, 1 Ryan Grant.
Replacements: 16 Pat MacArthur, 17 Jerry Yanuyanutawa, 18 Jon Welsh, 19 Leone Nakarawa, 20 James Eddie, 21 Ryan Wilson, 22 Niko Matawalu, 23 Duncan Weir.
Referee: George Clancy (Ire)
Assistant referees: Eddie Hogan-O'Connell, Kevin Beggs (both Ire)
TMO: Seamus Flannery (Ire)