Bath dug deep defensively to beat last term's Premiership finalists Exeter Chiefs and give Stuart Hooper his first league win as director of rugby.
Victory saw the hosts bounce back after their thumping 43-16 defeat away at Bristol in the season opener.
Converted tries from Chiefs' Jonny Hill and Bath's Tom Dunn plus penalties from Joe Simmonds and Rhys Priestland saw the sides level at 10-10 at half-time.
But Priestland's second penalty brought the only points of a tense second half.
The Chiefs, who were 22-19 winners at home to Harlequins in a hard-fought but somewhat unconvincing opening-weekend game last time out, were thwarted by a battling Bath pack.
The visitors were denied when just metres from the line on numerous occasion, as Hooper's side showed significant improvements from their poor display in their heavy loss at Ashton Gate.
Both sides were missing key players on the eve of the World Cup semi-finals, although Exeter gave a debut to Scotland full-back Stuart Hogg after his return from Japan.
Bath were again without South Africa's Francois Louw and England quintet Sam Underhill, Joe Cokanasiga, Jonathan Joseph, Ruaridh McConnochie and Anthony Watson, while the Chiefs were missing England trio Luke Cowan-Dickie, Jack Nowell and Henry Slade, plus Wales' Tomas Francis and Australia scrum-half Nic White.
Nevertheless, Friday's contest in soggy conditions at The Rec was bruising and intense, and the hosts - who finished 30 points behind Exeter last term - fought to get their campaign up and running.
The home side's kicking game was key and Priestland's pivotal role was decisive, as he shone in torrential West Country rain.
Crucially, with 13 minutes to go, Bath's Zach Mercer brilliantly denied Alex Cuthbert as he bundled the Welshman in to touch just two metres out after an excellent solo run looked set to end in a match-winning try.
Bath: Homer; Rokoduguni, Wright, Roberts, Brew; Priestland, Chudley; Obano, Dunn, Stuart, McNally, Ewels (capt), Williams, Ellis, Mercer.
Replacements: Walker, Boyce, Judge, Stooke, Bayliss, Cook, Burns, Hamer-Webb.
Exeter: Hogg; O'Flaherty, Whitten, S Hill, Cuthbert; J Simmonds, Maunder; Moon, Yeandle (capt), Williams, Dennis, J Hill, Ewers, Vermeulen, S Simmonds.
Replacements: Taione, Hepburn, Street, Kirsten, Kvesic, Townsend, Steenson, Hendrickson
Referee: JP Doyle