George Ford kicked all Bath's points to give them their eighth straight win in all competitions at a sold-out Recreation Ground on Saturday.
The young fly-half did not miss a single kick, converting six penalties and also dropping a goal to cement Bath's third place in the Aviva Premiership.
Exeter pushed them all the way in a typically hard-fought West Country derby, scoring two tries through locks Damian Welch and Dean Mumm, while fly-half Gareth Steenson kicked the rest of their points.
The visitors played plenty of positive rugby, but still they cannot find a way to beat their local rivals. Bath are the only Premiership club not to have lost to Exeter since the Devon club won promotion in 2010.
South Africa flanker Francois Louw returned to bolster the Bath pack and Horacio Agulla was also back from international duty with Argentina to wear the number 14 shirt. England prospect Anthony Watson replaced Nick Abendanon at full-back and Dom Day came in for the injured Stuart Hooper at lock.
Luke Arscott was making his first league start of the season for Exeter and Jason Shoemark returned at centre. Ben Moon replaced Brett Sturgess at loosehead prop.
Exeter drew first blood after after Jack Nowell carved through from a slick move off a line-out. Mumm was in support but was tackled early by Matt Garvey and Steenson kicked a sixth-minute penalty.
Ford equalised with a 40-metre penalty five minutes later after prop Hoani Tui was caught offside by a ricochet but Bath, while enjoying a considerable territorial advantage, had very little possession.
When Exeter did threaten the Bath 22, moving the ball left and right through many phases, the home defence at first covered effectively.
But, as so often happens, it was an attack from deep that found them out, Arscott fielding a long kick from Ford to set Matt Jess away on an arcing run. Welch was on his shoulder to evade Garvey on the touchline and the big lock came inside Peter Stringer to stretch out a long arm to score in Anthony Watson's tackle. Steenson's conversion attempt was wide but the visitors fully deserved their 8-3 lead after 23 minutes.
Bath hit back almost immediately with another Ford penalty and began to gain an edge in the scrum.
But they found it difficult to hang on to the ball in the face of a barrage of big hits from the Chiefs' defenders.
It was something of a relief, therefore, when Ford was presented with a 50-metre kick on the stroke of half-time and it cleared the bar with ease to give Bath a 9-8 interval lead.
They came out for the second half with ferocious intent, forcing three penalties in the visitors' 22, and having a catch-and-drive held up over the try-line, but Exeter successfully repelled the assault, led by Louw, Matt Banahan and Agulla.
Wales prop Paul James came off the bench for Catt as early as the 46th minute to further reinforce Bath's set-piece and Exeter promptly conceded a scrum penalty. Another offence further upfield saw Ford make it 12-8 from 40 metres on 53 minutes.
But Exeter hit back a couple of minutes later as Ford flapped at a pass from Stringer and Mumm hacked on a loose ball to win the race to the touchdown. Steenson's conversion hit the post.
Exeter's indiscipline at the scrum cost them again on 62 minutes as Ford knocked over another huge kick from half-way to edge Bath 15-13 ahead and yet another penalty allowed the young fly-half to pin the Devon side back into their 22.
Bath were beginning to find some rhythm and neat interpassing gave Ford just the glimpse of the posts that he needed to drop a goal on 68 minutes. Back came Steenson two minutes later with a penalty to cut the lead to two points but, given another chance five minutes later, his effort glanced the right post.
The tension continued to build as Bath attacked out of their own 22 and won a penalty of their own, again converted by the faultless Ford, with three minutes left on the clock.
Exeter had one last play to snatch a converted try for victory but conceded their ninth penalty of the second half - and Ford was able to kick the ball dead.