Glasgow responded perfectly from last week's hammering at Toulon with a 20-16 win over Exeter Chiefs on Sunday.
After their impressive triumph over Cardiff Blues last week, Exeter produced yet another composed display in the first period to take a 9-6 lead at the break, thanks to three Gareth Steenson penalties to Ruaridh Jackson's two.
But Tim Swinson and Tyrone Holmes touchdowns took the scoreline to 20-9 in Glasgow's favour before Dave Ewers earned the Chiefs a bonus-point when he crossed the whitewash.
The Warriors were looking for a better start than the one they produced against Toulon in round one of the Heineken Cup when the Scottish outfit found themselves 34-0 down at half-time.
However, it was the visitors that opened the scoring through the boot of Steenson, but the Chiefs don't have the firepower of the French giants and Glasgow were able to ease themselves into the game.
Jackson immediately restored parity with one of his own before the fly-halves traded penalties as the match remained finely poised at 6-6 after 14 minutes.
The visiting fly-half put them back into the lead with a three-pointer, but he was then sin-binned for a cynical infringement.
But the hosts weren't able to take advantage as Rob Baxter's men held on for a 9-6 lead at the break.
Gregor Townsend's men started well in the second period and Niko Matawalu was the inspiration for the first try of the encounter as the scrum-half off-loaded to Swinson who touched down.
And the victory was effectively sealed when a sweeping move ended in Holmes crossing the whitewash. Although Ewers touched down for the Chiefs for the losing bonus-point, Glasgow saw out the remaining minutes for a crucial win.
Tries: Swinson, Holmes
Con: Jackson 2
Pen: Jackson 2
Pen: Steenson 3
Glasgow Warriors: 15 Sean Maitland, 14 Tommy Seymour, 13 Byron McGuigan, 12 Gabriel Ascarate, 11 DTH van der Merwe, 10 Ruaridh Jackson, 9 Niko Matawalu, 8 Josh Strauss, 7 Tyrone Holmes, 6 Rob Harley, 5 Al Kellock (c), 4 Tim Swinson, 3 Ed Kalman, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Dougie Hall, 17 Jerry Yanuyanutawa, 18 Moray Low, 19 Jonny Gray, 20 Richie Vernon, 21 Chris Cusiter, 22 Duncan Weir, 23 Mark Bennett.
Exeter Chiefs: 15 Phil Dollman, 14 Ian Whitten, 13 Jason Shoemark, 12 Sam Hill, 11 Matt Jess, 10 Gareth Steenson, 9 Dave Lewis, 8 Dave Ewers, 7 Ben White, 6 Tom Johnson, 5 Damian Welch, 4 Dean Mumm (capt), 3 Hoani Tui, 2 Chris Whitehead, 1 Ben Moon.
Replacements: 16 Jack Yeandle, 17 Brett Sturgess, 18 Alex Brown, 19 Don Armand, 20 Kai Horstmann, 21 Haydn Thomas, 22 Henry Slade, 23 Fetu'u Vainikolo.
Referee: Romain Poite