Bath boosted their hopes of Heineken Cup qualification with a scratchy 26-18 Premiership victory over their west country rivals Exeter.
Banahan scored one and set up centre Matt Carraro for another as they moved to within one point of sixth placed Harlequins with a game in hand.
Scrum-half Michael Claassens added a third with fly-half Butch James kicking 11 points. Exeter responded through tries from full-back Luke Arscott and winger Matt Jess with stand-off Gareth Steenson booting two penalties and a conversion.
With the play-offs all but out of their reach, it was Bath who found themselves behind through an early penalty from Steenson.
The Chiefs then extended that lead when Arscott beat Banahan in a foot race to touch down, Steenson missing the conversion.
The hosts hit back with James kicking a penalty, but the away side continued to press and wasted two chances through centre Sireli Naqelevuki and number eight Richard Baxter.
Bath made them pay for those missed opportunities reducing the gap to two points through the boot of James prior to the stand-off converting Banahan's try a minute before half-time.
After an indifferent first period, Bath started the second half at pace and Banahan provided a moment of brilliance as he fed Carraro, James adding the extras.
James and Steenson then traded penalties before flanker James Scaysbrook was sin-binned for the away side on the hour mark.
Exeter were down to 13 men for a brief period when Hoani Tui was also yellow carded for persistent scrum infringements. And Claassens added a third try for the hosts before Exeter had the final say when Jess went over with two minutes remaining.
Tries: Banahan, Carraro, Claassens
Pens: James 3
Tries: Arscott, Jess
Pens: Steenson 2
Bath: 15 Sam Vesty, 14 Matt Banahan, 13 Matt Carraro, 12 Shontayne Hape, 11 Nick Abendanon, 10 Butch James, 9 Michael Claassens, 8 Luke Watson, 7 Guy Mercer, 6 Stuart Hooper, 5 Danny Grewcock, 4 Peter Short, 3 David Wilson, 2 Lee Mears, 1 David Flatman.
Replacements: 16 Pieter Dixon, 17 Nathan Catt, 18 Duncan Bell, 19 Ignacio Fernandez Lobbe, 20 Josh Ovens, 21 Mark McMillan, 22 Nick Scott, 23 Jacques Boussuge.
Exeter: 15 Luke Arscott, 14 Matt Jess, 13 Jason Shoemark, 12 Sireli Naqelevuki, 11 Nic Sestaret, 10 Gareth Steenson, 9 Junior Poluleuligaga, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 Chad Slade, 4 Tom Hayes, 3 Hoani Tui, 2 Neil Clark, 1 Brett Sturgess.
Replacements: 16 Chris Whitehead, 17 Ben Moon, 18 Ignacio Elosu, 19 Dave Gannon, 20 James Phillip, 21 Garrick Cowley, 22 Phil Dollman, 23 Ignacio Mieres.