British and Irish Lions head coach Andy Farrell looked on at Sandy Park as Bath scored three tries in five first-half minutes to surge clear.
After an early penalty try for the visitors, Niall Annett, Josh Bayliss and Will Muir crossed for a 26-10 half-time lead.
Exeter rallied through wing Paul Brown-Bampoe's two tries but fell short of a comeback and they remain second bottom.
"I think it was a great advert for the Premiership today. You had the team number one on the log versus the team that was number nine, and you got a game like that," said Bath boss Johann van Graan.
"It was quite a physical game and it looked like a war zone in our changing room afterwards."
Tom Curry starred for Sale in a 43-29 win at Harlequins to move up to third in the table.
Curry's two tries plus scores from Luke Cowan-Dickie and Asher Opoku-Fordjour ensured the visitors had a bonus point wrapped up by half-time.
Jonny Hill, Jean-Luc du Preez and Tom Roebuck also crossed after the break as Harlequins' own four tries only counted for a bonus point in a blow to their play-off ambitions.
Saracens climbed into the top four as England hooker Theo Dan scored two in a 36-14 win at Gloucester.
Sarries had to come back from a 14-12 half-time deficit but scored 24 points without reply in the second half.