Bath maintained their grip on this fixture but only after their 14 men survived a ferocious comeback by Exeter.
None of the Chiefs who played were born when Exeter last got the better of their West Country rivals in the John Player Special Cup back in 1978. Yet rarely have they come closer after a second-half fightback that undeservedly came up short.
Bath looked to be chasing a bonus-point win when their outstanding captain, Francois Louw, scored his team's third try before the hour to open a 20-8 lead but were forced to dig deep, not least when Dan Hipkiss was shown a red card while sat in the sin-bin.
Exeter shook off their handling problems and Hipkiss paid for his team's indiscretions. That did not stop the centre stepping off the sin-bin and deflecting Stephen Donald's kick to touch into the crowd, preventing Exeter taking a quick lineout.
That left Bath's 14 men to weather the storm for the final 13 minutes. Club captain Stuart Hooper, on as a replacement following injury, twice came up trumps with telling tackles before Donald's late penalty released the pressure. Bath head coach Gary Gold said: "It wasn't the smartest thing to do. He was due to come back on and it would have made life easier had we had a good defender back on after 10 minutes rest."
Bath's imports laid the foundations with Paul James in the scrum and Louw playing well. With half-backs Michael Claasens and Stephen Donald on form, the likes of Hipkiss, Tom Biggs and Nick Abendanon thrived.
Ben Williams barged over inside three minutes and Kyle Eastmond followed. Exeter's Gareth Steenson had an off-day in front of goal, striking to the left, right and directly at the uprights.
Coach Rob Baxter said: "My frustration is not with losing the game, but with our first-half performance. We lacked decision-making and clarity and looked cagey from the start."
When they did keep hold, Exeter looked threatening as Tom Johnson sent over Brett Sturgess before the replacement Ignacio Mieres set up a nail-biting climax only to miss in the final minute as a losing bonus point cruelly eluded Exeter.
Bath N Abendanon; K Eastmond, D Hipkiss, B Williams (S Vesty, 70), T Biggs; S Donald, M Claassens; P James, L Mears (B Sharman, 72), D Wilson (A Perenise, 57), D Day (S Hooper, 55), D Attwood, C Fearns (W Skuse, 10-19, 24), B Skirving, F Louw (capt, N Catt, 68).
Exeter L Arscott; G Camacho, P Dollman, J Shoemark, M Jess; G Steenson (I Mieres, 53), H Thomas (K Barrett, 72); B Sturgess (B Moon, 63), S Alcott (C Whitehead, 52), C Rimmer, D Mumm, J Hanks (A Muldowney, 53), T Johnson, R Baxter (capt), J Scaysbrook.
Referee Wayne Barnes.
Tries: Williams, Eastmond, Louw
Pens: Donald 2
Tries: Sturgess, Mieres