Matt Carraro's try came in the opening minutes of the second half
Bath ended a run of three defeats and kept alive their hopes of a top six Premiership finish with a 26-18 win over Exeter at the Rec.
Luke Arscott's individual try and Gareth Steenson's penalty put Exeter ahead but Matt Banahan's bullish score just before half time turned the game.
Matt Carraro went over straight after the break before Michael Claassens scored with 10 minutes left.
Exeter hit back with a converted try by Matt Jess but it was not enough.
Although Bath emerged victorious this was far from a comprehensive win.
At times in the first half Bath appeared to buckle and any hope that this win will spur them onto a late charge for a play-off berth looks to be in vain.
Claassens was twice nearly gifted tries in the first half from charge downs - the first in the opening minutes but neither ended in a score.
Steenson claimed first blood from a penalty after a Bath scrum fell apart in front of the posts.
The Irishman then produced a great line break and raced clear but the Chiefs could not finish off the move as Carraro caught Jason Shoemark short of the line.
Arscott's score was no more than the visitors deserved and it was all of his own making as he first span out of a tackle in his own half and then chipped over the advancing Sam Vesty to gather the ball and score.
After Steenson added the conversion Claassens charged own Junior Polu clearance but Bath were turned over with the tryline beckoning.
James did put them into the game in the 24th minute with a penalty and then came to rescue soon after with a tap tackle to deny Sireli Naqelevuki a try.
Exeter's discipline allowed James to pull the score back to 8-6 before his pop pass to Banahan saw the England man race in under the posts and with the conversion it was 13-8 to the hosts.
After the break Bath came out transformed and a quick line-out and slick handling saw Carraro score three minutes in.
James missed the conversion but landed a penalty five minutes later which was cancelled out by another from Steenson's boot.
Ex-Bath man James Scaysbrook was sent to the sin-bin just before the hour mark for persistent infringements and when a series of scrums failed, the Chiefs tight-head prop Hoani Tui followed him to leave the Devon side with 13 men.
But Exeter held on for nearly 10 minutes before Nathan Catt burst out of his own 22 and made 50 metres before Claassens was on hand to finish off his good work.
James missed the conversion once more but Jess's try - converted by Ignacio Mieres - was a mere consolation.
Bath performance director Sir Ian McGeechan: "If we are winning then we can have a look at what everyone else is doing. If we keep losing, it doesn't matter what others are doing.
"We have to focus on the way we want to play, on what we have to do now. What we've got to do now is to focus on the next game against Harlequins. If we get it right again there's more pressure on the teams above us.
"The first 20 minutes could have been better. The second 20 of the first half and the first 20 of the second half we got somewhere we wanted to be.
"We were more focused on keeping the ball and building pressure. The outcome was two penalties and a try.
"The forwards stepped it up and worked hard. It was a hot day. And in the second half we were much more accurate and put Exeter under pressure."
Exeter Chiefs head coach Rob Baxter told BBC Radio Devon: "The thing that really disappointed us as a coaching staff was that for 20 minutes after half-time we just stopped playing and that really swung the whole momentum of the game away from us.
"When we attacked we looked a good side, we could find space and we could find holes, and yet we lost our confidence.
"It would have only taken for two things to have gone differently today and that result would have been very different, so that's a massive positive for us."
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