Exeter (9) 9
Pens: Steenson 3
Bath (6) 12
Pens: Barkley 4
Bath's Lee Mears prepares to tackle Exeter's captain Tommy Hayes
Four penalties from centre Olly Barkley handed Bath victory over Exeter in a tight encounter at Sandy Park.
Barkley and Chiefs fly-half Gareth Steenson traded penalties in a tense first-half which ended with the home side holding a 9-6 lead.
England international Barkley brought the scores level on 50 minutes, before Steenson put two penalty attempts wide.
As the game drifted towards its conclusion Barkley struck again to give his side the win.
The match promised much after a lively opening spell in which the capacity crowd at Sandy Park saw several line breaks from an Exeter side still buoyant having won their previous two Premiership matches.
Steenson broke the deadlock with a sixth minute penalty, before Barkley levelled things up with a kick from 40m.
Two further penalties from Steenson put Exeter 9-3 ahead but Barkley cut the deficit again just before the break with a second place kick after the Chiefs were penalised for coming into a ruck from the side.
Bath started to enjoy greater possession at the start of the second period, and after spending several minutes camped on Exeter's line, came close to scoring the game's opening try but Ben Williams knocked on when in clear sight of the whitewash.
With their defence having held firm, Exeter slowly became more assured again, using the strength of centre Fijian centre Sireli Naqelevuki to batter holes in Bath's defence.
Exeter's chance to regain the lead came with 10 minutes to play as Bath were penalised for offside but Steenson, usually ever reliable with the boot, pushed the resulting penalty agonisingly wide.
Another opportunity at goal for the Northern Irishman quickly arose, Bath's scrum buckling under pressure from the home pack.
But much to the agony of the the expectant crowd, Steenson's kick was wayward and the scores remained level.
Having been let of the hook, Bath seized the opportunity to attack, taking the play deep into Chiefs territory where after several minutes of pressure they were rewarded with a 78th-minute penalty from which Barkley made no mistake.
Exeter bravely tried to claw their way back into the match but time was against them as Bath used all of their experience to close out the game.
Exeter: Arscott; Jess, Shoemark, Naqelevuki, Sestaret; Steenson, Thomas; Sturgess, Clark, Budgen, Hayes, Hanks, Johnson, Scaysbrook, Baxter.
Replacements: Nadolo for Jess (77), Slade for Hanks (77), Phillips for Johnson (79).
Not Used: Alcott, Moon, Elosu, Poluleuligaga, Mieres.
Bath: Abendanon; Cuthbert, Williams, Barkley, Biggs; James, Claassens; Flatman, Mears, Bell, Hooper, Grewcock, Skirving, Watson, Taylor.
Replacements: Vesty for Abendanon (11), McMillan for Claassens (69), Barnes for Flatman (66), Dixon for Mears (61), Fernandez Lobbe for Grewcock (61).
Not Used: Palma-Newport, Mercer, Scott.
Ref: David Rose (RFU).