A late try from lock Richie Gray saw Glasgow snatch victory from Bath at Firhill as Stephen Donald was denied the match-winning tag in a 26-21 win.
With time up in Scotland, the soon-to-be Sale forward reacted quickest to a deflected Duncan Weir drop-goal attempt to score under the posts.
It had looked like new signing Stephen Donald had won the game for Bath with three points from the tee, but up stepped Gray in a thrilling finish.
Bath were dealt a blow before kick-off when Matt Banahan withdrew from the side injured, but it was their new centre partnership of Sam Vesty and Dan Hipkiss that caused the hosts several problems during the early stages. Forgotten England centre Hipkiss was a constant threat.
With New Zealander Donald occupying a place on the bench, it was instead young fly-half Tom Heathcote who ran from ten and it was he who opened the scoring in Glasgow with a well-struck penalty close to the left touchline. His opposite number Weir responded though two minutes later. Both were set to play major roles.
Bath were continuing to enjoy most of the territory as the half-hour approached and they were rewarded for their good work when Heathcote slotted another three, this time from the halfway line for his charges. What encouraged Bath was Tom Biggs growing into matters.
Glasgow did manage to assert some of their own pressure on the visitors' line though and on 33 minutes were awarded a penalty after Simon Taylor was pinged for not rolling away by French referee Christophe Berdos. Weir made no mistake and gladly levelled proceedings.
And they in fact went in at the break 9-6 up when Bath second-row Ryan Caldwell was penalised for reacting when Pat MacArthur raked the visiting captain Stuart Hooper.
The second-half began more or less as the first ended but this time Weir could not add three points after David Wilson was pinged for dropping his bind. Heathcote made no such mistake for Bath though as, from distance again, he slotted the match-levelling penalty with 44 minutes gone on the clock. 9-9 it was as things started to heat up in cold Scotland.
Heahtcote was showing no sign of nerves, even with future first-choice ten Donald looking on from the sidelines. The 19-year-old slotted over his fourth penalty for the lead at 12-9.
However, against the run of play, Glasgow scored the first try of the match as full-back Stuart Hogg went over on the hour mark and Weir converted for 16-12.
The metronomic Heathcote reduced the deficit to just one point with his fifth penalty two minutes later and sent Bath into the lead again in the 68th minute with his sixth successive penalty. He was promptly taken off and Donald came on for his debut.
However, it was Weir who struck next after he added a penalty following a good break by him which resulted in the Bath infringement to restore the Scottish side's one point lead.
In a topsy-turvy encounter Donald then sent Bath back into the lead with three minutes remaining as he landed a penalty leaving the hosts an uphill task to win the game.
But having set Weir up for the drop-goal attempt the fly-half made a lame attempt but the bounce of the ball fooled the Bath defence and fell kindly to Gray who went over under the posts to touch down - Weir added the extras to complete a remarkable end to the match.
Tries: Hogg, Gray
Con: Weir 2
Pen: Weir 4
Pen: Heathcote 6, Donald
Glasgow: 15 Stuart Hogg, 14 Tommy Seymour, 13 Rob Dewey, 12 Graeme Morrison, 11 Colin Shaw, 10 Duncan Weir, 9 Chris Cusiter, 8 Ryan Wilson, 7 John Barclay, 6 Rob Harley, 5 Alastair Kellock, 4 Richie Gray, 3 Michael Cusack, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Dougie Hall, 17 Gordon Reid, 18 Ed Kalman, 19 Tom Ryder, 20 Chris Fusaro, 21 Henry Pyrgos, 22 Troy Nathan, 23 Federico Aramburu.
Bath: 15 Nick Abendanon, 14 Olly Woodburn, 13 Dan Hipkiss, 12 Matt Banahan, 11 Tom Biggs, 10 Tom Heathcote, 9 Michael Claassens, 8 Simon Taylor, 7 Guy Mercer, 6 Francois Louw, 5 Ryan Caldwell, 4 Stuart Hooper, 3 David Wilson, 2 Ross Batty, 1 David Flatman.
Replacements: 16 Kane Palma Newport, 17 Charlie Beech, 18 Anthony Perenise, 19 David Attwood, 20 Will Spencer, 21 Mark McMillan, 22 Stephen Donald, 23 Sam Vesty.
Referee: Christophe Berdos (France)