Priestland boot sinks Scarlets
The Welshman's near flawless kicking performance ensured his England club, Bath, made it two wins out of two in Europe.
Scarlets, the pre-match favourites, could not get their running game going in the atrocious conditions and also lacked the ability to make adjustments.
Bath simply played the rainy conditions better – applying the pressure, with scrumhalf Kahn Fotuali'i keeping his team on the front foot with an educated boot.
Priestland – who scored 1,102 points in 157 matches during his spell in Llanelli – kicked six of his penalty shots at goal.
Scarlets had briefly taken the lead on 22 minutes with a brilliant team try, finished off by Steff Evans, with the TMO adjudging a pass in the build-up to be legal.
But on a foul night of incessant rain in west Wales, Scarlets could not fashion try-scoring opportunities in the second half as Bath's defence held firm.
Bath have now won 10 of their last 13 against Welsh opposition in the competition, although they had not played against the regions since the 2008/09 pool stage when they faced the Dragons.
Bath set out their stall through the opening phases when Toby Faletau broke down the touchline to give the visitors a foothold deep in Scarlets' territory.
When there, they proved hard to shift and that territory yielded penalties.
With the rain streaming down, Bath's work in attack was often neat and accurate, despite the greasy conditions. And after a series of phases that stretched the Scarlets' defence, Roman Poite awarded Todd Blackadder's side a penalty.
Priestland converted, but Leigh Halfpenny almost immediately replied for Scarlets after Bath conceded a scrum penalty on the restart.
Still, the error count was already mounting – understandably so, considering the terrible conditions – and Priestland extended Bath's lead to leave the visitors in front 6-3 after 10 minutes.
Scarlets' wing Steff Evans scored the only – albeit a spectacular – try after the home side's adventurous running and audacious handling was rewarded by a surging line-break from Evans, who then passed back inside to Gareth Davies on his shoulder. Evans then collected the popped return to streak over under the posts.
Roman Poite consulted the TMO to check for a forward pass. But the score stood.
For the Scarlets:
Pens: Halfpenny 2
Pens: Priestland 6
Scarlets: 15 Leigh Halfpenny, 14 Johnny Mcnicholl, 13 Jonathan Davies, 12 Hadleigh Parkes, 11 Steff Evans, 10 Rhys Patchell, 9 Gareth Davies, 8 Tadhg Beirne, 7 Will Boyde, 6 Aaron Shingler, 5 Lewis Rawlins, 4 Jake Ball, 3 Samson Lee, 2 Ken Owens (captain), 1 Wyn Jones.
Replacements: 16 Ryan Elias, 17 Dylan Evans, 18 Werner Kruger, 19 David Bulbring, 20 Josh Macleod, 21 Jonathan Evans, 22 Paul Asquith, 23 Scott Williams.
Bath: 15 Anthony Watson, 14 Semesa Rokoduguni, 13 Jonathan Joseph, 12 Max Clark, 11 Aled Brew, 10 Rhys Priestland, 9 Kahn Fotuali’i, 8 Taulupe Faletau, 7 Sam Underhill, 6 Zach Mercer, 5 Luke Charteris, 4 Charlie Ewels (captain), 3 Anthony Perenise, 2 Tom Dunn, 1 Beno Obano.
Replacements: 16 Jack Walker, 17 Nathan Catt, 18 Scott Andrews, 19 Elliott Stooke, 20 Paul Grant, 21 Darren Allinson, 22 Josh Lewis, 23 Matt Banahan.
Referee: Romain Poite (France)
Assistant referees: Pierre Brousset (France), Stephane Boyer (France)
TMO: Eric Gauzins (France)