England fly-half George Ford ensured that Bath launched their European Champions Cup campaign in winning fashion at the Recreation Ground - but Irish heavyweights Leinster are lurching towards an early exit.
Leinster, crushed 33-6 at home by Pool Five opponents Wasps last Sunday, have now lost their opening two games of a European campaign for the first time since 1996 as Bath triumphed 19-16.
And with Champions Cup holders Toulon also in the toughest group of this season's tournament, Leinster are already struggling to progress, even if it took a 76th-minute Ford penalty to deny them a draw.
Ford sent an early reminder to new England head coach Eddie Jones of his quality by booting 14 points - three penalties, a conversion and a drop-goal - as Bath also collected a second-half penalty try.
Ireland star Johnny Sexton kicked 11 points for Leinster, including the conversion of substitute back-row forward Josh van der Flier's late try, but Bath had done enough.
They now face home and away European appointments with Aviva Premiership rivals Wasps next month, and while they will be disappointed after failing to convert many of their chances into points, it was still a key win.
Bath's Wales international lock Dominic Day was ruled out due to appendicitis, so Stuart Hooper featured in the starting line-up and captained a side that opened its Champions Cup campaign after last Sunday's scheduled opener in Toulon was postponed following the Paris terror attacks.
Leinster head coach Leo Cullen reacted to the Wasps defeat by changing more than half his starting line-up, and Bath made all the early running, with wing Semesa Rokoduguni leading a promising early break deep into opposition territory.
But when Hooper infringed at an eighth-minute ruck, Sexton kicked Leinster ahead with ease from 40 metres, only for Ford to land an equalising penalty and then kick a drop-goal six minutes later as Bath looked to make their possession monopoly count.
Leinster had not been in the game as an attacking force, and they were fortunate not to fall further behind seven minutes before the break when impressive Bath wing Matt Banahan ran strongly from just inside Leinster's half.
Banahan's power ensured that Bath got behind the Leinster defence, yet after centre Kyle Eastmond shipped out possession, a Banahan knock-on as he delivered a scoring pass to an unmarked Hooper meant that Leinster escaped.
The visitors enjoyed their best spell as half-time approached, but they could not add to Sexton's early penalty and Bath trooped off with a 6-3 interval lead that should have been considerably more, given the amount of ball they had.
Ford launched the second period by making a slashing midfield break, yet the fact it ultimately came to nothing summed up an opening 45 minutes when Bath's intent was not matched by deed.
Ford and Sexton then exchanged penalties in quick succession as Bath moved 9-6 ahead, and that was the cue for Cullen to change both his props, with Jack McGrath replacing Cian Healy and Martin Moore taking from Mike Ross.
Sexton completed his penalty hat-trick to tie the scoreline, but Bath's forwards had started to enjoy a clear upper hand, which was underlined when referee Jerome Garces awarded them a 62nd-minute penalty try.
Leinster could not cope with Bath pressure from a set-scrum near their own line, and Garces' patience ran out following a second reset scrum, with Ford's conversion opening up a seven-point advantage.
But Leinster fought back impressively, and a flowing attack ended in Van der Flier touching down, with Sexton adding the extras to again level things up.
It ensured a frantic final 10 minutes launched by Sexton missing a penalty from just inside his own half, but Ford came up trumps with just four minutes remaining and Leinster were left with just a losing bonus point for their efforts.