Bath completed a Heineken Cup double over a gutsy Glasgow side
Glasgow (13) 19
Try: Gregor Cons: Parks Pens: Parks 3, Jackson
Bath (8) 25
Tries: Banahan 2, Berne, Maddock Cons: James Pens: James
Matt Banahan was the two-try hero for Bath as the visitors completed a narrow Heineken Cup double over Glasgow.
The winger broke through in each half to keep alive Bath's hopes of reaching the knock-out phase.
Colin Gregor touched down for Glasgow and the kicking of Dan Parks gave the hosts a half-time lead.
Shaun Berne claimed Bath's second try after the break and Joe Maddock sealed the win with the fourth score for the English side late in the game.
Glasgow were dealt a blow in the build-up when winger Thom Evans, who claimed three tries in the reverse fixture last week, pulled up with an ankle injury.
The action was disjointed in the opening sparring session with the Parks swapping penalties with opposite number Butch James.
James then unleashed a perfectly-weighted cross-kick for Banahan to claim the first touchdown.
James was wide with the angled conversion and then committed a fearful blunder to present Glasgow with a try.
The South African lost control when under no significant pressure, allowing Gregor to pounce from close quarters.
The Glasgow scrum-half hacked the ball over the line and followed up to get the vital touch, with Parks banging over the conversion to put his team ahead.
Parks confidently added a penalty to establish a 13-8 lead at the halfway point.
Bath were more spirited after the restart and it was no surprise when they created a fine second score.
Following a series of patient and well-controlled phases, centre Berne was in the right place at the right time to finish in style and tie the contest.
Parks immediately reclaimed the advantage for the Warriors with his third penalty.
As in last weekend's tussle, play was flowing from end to end and Bath seized the initiative again midway through the half through the bulky Banahan.
But a high challenge by James on Max Evans gave sub Ruaridh Jackson the penalty to edge the home side in front.
However, Joe Maddock skidded over for the clincher with six minutes remaining and James landed the goal.
Bath coach Steve Meehan: "We had more control of the game this time round compared to last week's match at The Rec.
"But Glasgow are a very, very good side and any team who fails to give them due respect will come unstuck.
"We now have a long wait for the Newport meeting and it will be a key fixture for us.
"It is up in the air who will qualify from this group, but with our injury situation improving all the time, I have to be confident about our prospects of moving forward."
Glasgow coach Sean Lineen: "We never established a platform and in the second half we were unable to create a meaningful try opportunity.
"We were buzzing at half-time, but we didn't win enough possession after the restart to mount any real threat.
"Our scrum was not as good as it should have been and at times the lineout did not function.
"When we did get the ball, we couldn't keep it long enough to put Bath under pressure."
GlasgowWarriors: Stortoni, Faatau, M. Evans, Henderson, O'Hare, Parks, Gregor, Va'a, Thomson, Low, Barker, Turner, Brown, Barclay, Beattie.
Replacements: Nunez Piossek for Faatau (30), Jackson for Parks (61), Pinder for Gregor (61), Milligan for Thomson (63), Tckachuk for Low (40), Forrester for Beattie (75). Not Used: Palepoi.
Bath: Abendanon, Maddock, Berne, Fuimaono-Sapolu, Banahan, James, Claassens, Barnes, Dixon, Stevens, Harrison, Grewcock, Beattie, Lipman, Browne.
Replacements: Crockett for Berne (67), Bell for Barnes (72), Mears for Dixon (48), Faamatuainu for Beattie (58). Not Used: Hooper, Bemand, Cuthbert.
Ref: C Berdos (France)