Bath were made to work hard by Exeter but eventually emerged with a deserved 23-15 Premiership victory at the Recreation Ground on Saturday.
The home side started like a train, controlling possession from the outset, and it didn't take them long to hit the front.
Nick Abendanon's jinking run set up Ben Williams to score in the right-hand corner after Gonzalo Camacho had missed two tackles in quick succession.
They weren't the last tackles the Chiefs would miss either as they struggled to deal with the relentless waves of attacks from the hosts.
Several defenders made a meal of bringing down Francois Louw after quarter of an hour and that allowed Stephen Donald to find Kyle Eastmond in acres of space on the right wing and he coasted over in the corner.
The visitors finally got some possession midway through the half and they did briefly show a glimpse of the form that has made them the second top try-scorers in the league this season, with Jason Shoemark and Tom Johnson giving Brett Sturgess the chance to trundle over in the corner.
Bath were dominant for the most part though and they added a late penalty from World Cup-winning fly-half Donald to make it 15-5 at the break.
Exeter improved in the early stages of the second half and reduced the deficit with a Steenson penalty but the hosts hit them with another killer blow moments later as the impressive Eastmond and Abendanon shipped the ball out for Louw to score.
Still the Chiefs refused to lie down though and, after Dan Hipkiss was sent to the sin bin with quarter of an hour remaining, replacement Ignacio Mieres took advantage of the extra man by using an overlap as a decoy and stepping inside Tom Biggs to score.
Hipkiss never re-entered the fray as he was given a second yellow card whilst in the sin bin for getting involved and interfering with the ball when he shouldn't have and that added to a nervous end to the match for his side.
A late Donald penalty made the victory safe though and, despite an almost endless period of added time as the hosts pushed for a bonus point try and Exeter looked for a losing bonus point, that was the final score of the game and Bath deservedly recorded their fourth win of the campaign.
Tries: Williams, Eastmond, Louw
Pens: Donald 2
Tries: Sturgess, Mieres
Yellow card: Hipkiss (Bath - 66th min)
Red card: Hipkiss (Bath - 74th min)
Bath: 15 Nick Abendanon, 14 Kyle Eastmond, 13 Dan Hipkiss, 12 Ben Williams, 11 Tom Biggs, 10 Stephen Donald, 9 Michael Claassens, 8 Ben Skirving, 7 Francois Louw (c), 6 Carl Fearns, 5 Dave Attwood, 4 Dominic Day, 3 David Wilson, 2 Lee Mears, 1 Paul James.
Replacements: 16 Brett Sharman, 17 Nathan Catt, 18 Anthony Perenise, 19 Stuart Hooper, 20 Will Skuse, 21 Mark McMillan, 22 Sam Vesty, 23 Horacio Agulla.
Exeter: 15 Luke Arscott, 14 Gonzalo Camacho, 13 Phil Dollman, 12 Jason Shoemark, 11 Matt Jess, 10 Gareth Steenson, 9 Haydn Thomas, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 James Hanks, 4 Dean Mumm, 3 Carl Rimmer, 2 Simon Alcott, 1 Brett Sturgess.
Replacements: 16 Chris Whitehead, 17 Ben Moon, 18 Chris Budgen, 19 Aly Muldowney, 20 Dave Ewers, 21 Kevin Barrett, 22 Ignacio Mieres, 23 Ian Whitten.
Venue: Recreation Ground
Referee: Wayne Barnes
Assistant referees: Paul Dix, Robin Goodliffe
Television match official: Geoffrey Warren