New signing Peter Stringer came off the bench on his Bath debut to score both tries in a scrum-half masterclass against Exeter at the Recreation Ground.
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Ireland international Stringer, who had arrived on loan from Munster earlier in the week, had spent 38 minutes watching Exeter dominate much of the first half of this LV=Cup clash while Bath looked anything but the home team.
However, the 35-year-old crossed twice in the second half to earn Bath the victory.
It was Exeter's first defeat in this season's LV=Cup and they still have not beaten their west country rivals in a competitive match since 1978.
It had started well enough for Bath as Tom Heathcote opened the scoring with a fourth-minute penalty. But that was soon cancelled out by Henry Slade and Exeter, fielding an entirely different XV from the team beaten by Leinster last week, were quickly into their stride.
Bath led a charmed life as visiting lock Damian Welch had a try ruled out for a forward pass and scrum-half Will Chudley was held just short of the line.
Exeter had to wait until the 23rd minute for the score their play deserved but it was only another Slade penalty after a mix-up at the back of a ruck, where Mark McMillan was being hounded by Chudley.
On a rare visit to the visitors' 22 Bath managed to spoil an Exeter scrum - neither side was comfortable on their own ball - and Heathcote made it 6-6 from the resulting penalty on 31 minutes. Ben Williams was then laid out attempting a tackle and was replaced by Sam Vesty.
With Nic Sestaret in threatening form, Exeter mounted another series of dangerous attacks as half-time approached but prop Craig Mitchell was just crowded out at the corner.
Then came Stringer's arrival, on for McMillan, and he was immediately a calming influence for Bath.
England hooker Rob Webber, recruited from Wasps last summer, was restricted to just 40 minutes on his first outing for Bath after shoulder surgery and Stringer needed treatment early in the second half after falling on to the ball.
But he dragged himself back to his feet and got back to the task of prompting and urging Bath into a far more convincing second half performance.
Mat Gilbert came closest to scoring on 50 minutes with a drive to the line, supported by Nick Koster, but Exeter held out and cleared their lines - although not for long.
Bath earned a kickable penalty but opted for the line-out and although Exeter stopped the catch and drive, Stringer dived through to touch down on 56 minutes. Heathcote's conversion was wide but they were quickly back on the attack and Dave Attwood nearly scored after Stringer sniped around a ruck.
Moments later, Chiefs' blindside defence was found wanting again and Stringer grabbed his second try, again unconverted.
Exeter came back strongly but lacked composure close to the line when it seemed they must score.