Saints got off to the worst possible start. They may have gathered the kick off, gone through a couple of phases and cleared their lines, but Bath had great position midway between the visitors' 22 and 10-metre lines which they used to the full.
The initial midfield charges were held comfortably, but at the second phase Olly Barkley sent the ball fizzing behind the dummy runners to Tom Biggs to spread the play. Biggs slid through a grubber, which sat up superbly for full back Nick Abendanon to cross unopposed in the left corner.
Saints showed their composure by working their way into position from which Stephen Myler landed three points, but Bath were soon back in the visitors' red zone and five points ahead courtesy of Olly Barkley's immediate reply.
Bath were certainly up for the contest, and were perhaps a touch unfortunate when the first man of a powerful ruck was deemed to have flopped on Vasily Artemyev after the Russian had collected a Michael Claassens box kick well under pressure.
But strokes of fortune need to be capitalised on, and when Saints went through the phases - Luther Burrell and Samu Manoa both notable carriers - they quickly earned another penalty for Myler to pull three points back.
The first quarter may have been end-to-end, but it had been far from frenetic as both teams patiently used their respective spells of possession to work their way upfield and into scoring positions.
However the next three points required the least amount of effort. Having awarded a Saints a scrum when Lee Mears miss-threw a lineout, referee Andrew Small lost his patience when Bath then refused to disengage for a re-set. Up stepped Myler and the visitors had the lead for the first time.
It was not just the scoring chances which were alternating between the teams. The luck was swinging both ways, too. First Saints were let off when Dan Hipkiss fumbled at the base of a ruck five metres out from the visitors' line. Then at the other end Abendanon somehow got a bounce which took his clearance kick from the corner some 50 metres upfield.
Myler's deftness with the boot had put Abendanon under pressure in the first place, and when he continued his 100 percent record from the tee Saints had a small amount of breathing space for the first time. There was another scare as Bath looked to finish the half as they had started it, but Barkley's penalty hit the left-hand upright and the teams headed for the break with Saints leading 12-8.
Biggs had been Bath's most potent runner in the first half. But he also proved to be Saints' biggest obstacle in the opening minutes of the second, inadvertently treading on Ben Foden's foot to force the full back off, then clattering into Dom Waldouck while attempting an interception five metres out from his own line.
Foden's injury aside, Saints were having their best spell of dominance, pushing Bath back to their own line with some controlled play and powerful carries. However while Myler landed his fifth penalty it seemed scant reward, especially when Barkley landed his second three-pointer the first time Bath visited the other end of the field.
Six minutes later Barkley was on target again, the margin was back down to one and the contest was back on a knife-edge. A pair of missed Myler kicks - the first a long-range drop-goal, the second a penalty from a similar position - did nothing to help the travellers' nerves, and as the last 10 minutes approached it looked like just the one mistake this way or the other would be the deciding factor.
Nerves certainly seemed to be playing their part. Barkley miss-hit a penalty in the 69th minute, then Bath caught Saints' lineout yips, completely messing up a throw on the visitors' 10-metre line.
Despite this Bath were looking good for points. But yet again a turnover proved crucial, this time Aviva man of the match Manoa charging down a Barkley kick and running to the line. Tom Wood was on the American's shoulder, but the flanker was pulled down agonizingly short and instead had to be content with Tom May's smartly taken drop-goal.
Although the replacement had got the much needed points there was still time for yet more drama. Runs from Abendanon and Dominic Day took Bath within sight of the Saints' line, and when Barkley kicked a penalty to the corner with less than two minutes to play The Rec was set for a grandstand finish.
Phase after phase Bath carried, only to come up against a Saints defence that yet again this season showed its character, and when Ben Skirving fumbled with 30 seconds to go all the visitors had to do was count out the clock and take home the points.
2mins BATH Try Abendanon 5-0
7mins SAINTS Pen Myler 5-3
10mins BATH Pen Barkley 8-3
16mins SAINTS Pen Myler 8-6
22mins SAINTS Pen Myler 8-9
36mins SAINTS Pen Myler 8-12
40mins BATH Miss pen Barkley
HALF-TIME BATH 8 SAINTS 12
50mins SAINTS Pen Myler 8-15
53mins BATH Pen Barkley 11-15
59mins BATH Pen Barkley 14-15
62mins SAINTS Miss DG Myler
65mins SAINTS Miss pen Myler
69mins BATH Miss pen Barkley
76mins SAINTS DG May 14-18
FULL-TIME BATH 14 SAINTS 18