Bath had held a 10-6 lead on Saturday after a turgid opening half thanks to a Tom Biggs try and five points from centre Olly Barkley's boot, fly-half Duncan Weir replying with two penalties for the visitors.
The second half mercifully proved to be a far more entertaining affair. Ben Skirving's converted try extended Bath's lead before Glasgow turned the game on its head as wing Tommy Seymour and flanker Rob Harley crossed.
But Barkley had the last word as he claimed a personal haul of 13 points to give the hosts just a second win in nine games, and end Glasgow's lingering hopes of an Amlin Challenge Cup quarter-final spot.
With both sides having no hope of progressing in this tournament The Rec crowd may have hoped to see an enterprising tussle, but they were instead treating to stodgy, error-strewn fare during the first 40 minutes.
Weir had booted the Warriors into a third-minute lead with his first penalty, but it was his error that gifted Biggs the opening score.
The outside-half looked to shift the ball on while under pressure, and his loose pass was gathered in by Biggs who raced in from halfway for a try converted by Barkley.
Scrum-half Chris Cusiter's chargedown of opposite number Chris Cook quickly put Bath on the back foot and forced a second penalty for Weir to convert, but the Scottish side were already showing signs of struggling to handle the home pack.
The Warriors front row of Jon Welsh, Pat McCarthur and Ed Kalman were under constant pressure at scrum time, conceding a string of penalties, while Bath's driving maul was proving an effective weapon.
Barkley extended the home side's lead to four points in the 17th minute with his second penalty, after John Barclay was harshly penalised for not rolling away, but a lack of accuracy at crucial moments meant Bath did not take advantage of their forward edge.
Countless promising attacking positions went begging, either from crooked line-out throws or clumsy handling, and their half-time lead would have been just a single point had Weir being able to land a difficult long-range penalty effort just before the interval.
But Bath finally made the dominance of their pack tell four minutes into the second stanza as a well-controlled, trundling maul worked its way over from fully 25 yards, with Skirving emerging from the heap of bodies to claim the score. Barkley added the extras with the help of an upright.
There were injury worries for Scotland coach Andy Robinson as prop Ed Kalman joined lock Ali Kellock in being forced but, against the odds, Glasgow almost found an instant reply after referee Christophe Berdos somehow missed McCarthur's crooked throw at a line-out on halfway.
Barclay cut through the Bath midfield and smart handling sent wing Colin Shaw over, only for the final pass to be ruled forward.
But the Warriors did strike back after the most cohesive period of attacking play in the entire contest as they stretched Bath one way and then the other to create a weight of numbers that allowed replacement Scott Wight to give Seymour an easy finish.
Wight, on for Weir, knocked over the conversion to trim the lead to four and Glasgow's fightback was given added impetus when Cook was sin-binned for killing the ball.
And the Warriors second try was not long in coming as centre Stuart Hogg streaked down the right to second back-rower Harley over to put Glasgow a point to the good with 17 minutes to play.
But having fought so valiantly to get back in the game the Warriors were caught trying to play their way out of their own half, and Barkley punished them with another penalty to put Bath back ahead, before adding another three-pointer in the dying minutes.
In the day's other Pool Three clash, already-qualified Leinster won 25-3 at home to Montpellier with tries from Sean O'Brien, Rob Kearney and Cian Healy.
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