The conversion of a penalty try three minutes from time denied Exeter their first Premiership victory over west country rivals Bath in front of a sell-out crowd of 10,744 at Sandy Park.
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Both sides went into the game on the back of defeats with Exeter seeing their run of seven victories halted by a 18-16 defeat at Gloucester while Bath were hammered 22-0 at home to Saracens.
Tom Hayes returned to the second row to lead the Chiefs while Phil Dollman came in at outside centre so James Hanks and Ian Whitten dropped to the bench where they were joined by the return of England international Tom Johnson.
Full back Ollie Devoto made his first Premiership start for Bath while inside centre Matt Banahan, locks Dave Attwood and Ryan Caldwell and number eight Ben Skirving all returned to action for the visitors.
The Chiefs applied the early pressure but conceded silly penalties and when close to the posts they had the ball turned over. Then with 12 minutes on the clock fly-half Gareth Steenson, with the wind at his back, landed the opening penalty.
But the visitors hit back immediately with a try started and finished by scrum half Michael Claassens in the left corner with great support play from wing Tom Biggs and fly-half Steven Donald. Claassens was unable to convert from touchline.
Exeter wasted a try scoring opportunity when full back Luke Arscott made the break through the middle and, with scrum half Hayden Thomas on his right in space, he passed to lock Aly Muldowney who was quickly brought to ground.
The home side were able to create breaks from deep in their own half but unforced errors or penalties were again the Chiefs downfall when they ventured into the Bath 22 allowing the visitors to keep their line intact.
Then, with time already up on the clock, Bath wing Horacio Agulla was penalised for coming in at the side of the ruck and Steenson stepped-up to land his second kick of the game and nudge the Chiefs into a 6-5 half-time lead.
Steenson increased the lead minutes after the restart when Bath repeated the previous offence just before the break but this time Skirving was the culprit. The penalty from the former Ireland under-21 took him past 1,000 points since his Exeter debut in 2008.
The Chiefs were certainly an improved side in the second half at the scrum and the lineout as well as limiting their errors. Bath strayed offside when inside their own 22 and Steenson kept a clean sheet with his fourth penalty kick.
Exeter again showed that they too can defend their own line and with the game going into the final 10 minutes the Chiefs again camped out inside the Bath 22. But when they turned a Bath scrum the home side were penalised for standing up.
Bath won a penalty inside the Exeter 22 and opt to kick for the corner and then the Chiefs were penalised at the ruck. Bath repeated the move and referee David Rose awarded a penalty try. Tom Heathcote added the extras to level the score.