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The Prem
Bristol (10) 20
Tries: Ibitoye, Ivanishvili Cons: Williams 2 Pens: Williams 2
Exeter (0) 7
Tries: Fisilau Cons: Slade
Bristol moved up to third place in the Prem after beating Exeter 20-7 at Ashton Gate.
Gabriel Ibitoye's 26th-minute try and James Williams' penalty three minutes later were the only scores of an attritional first half in difficult conditions.
Greg Fisilau was mauled over 12 minutes after the restart as Exeter got on the scoreboard.
The Chiefs tried to force a second, but it was Bristol that earned the win when Williams kicked an excellent 41-metre penalty before Luca Ivanishvili crashed over from close range after Olly Woodburn had fumbled a high ball.
His late try denied Exeter a losing bonus point and leaves Rob Baxter's side in ninth place on eight points, six behind the Bears.
The stormy weather's impact was in evidence from the first whistle as both sides struggled to keep hold of the ball.
Bristol almost scored in the opening 60 seconds after an Exeter mistake under a kick saw the ball bobble around in their in-goal area.
It was as close as either side came to scoring in the opening 26 minutes as the hosts had the better of the possession and territory but were stifled by a spirited Exeter defence.
The pressure finally told when Ibitoye got on the end of a looping Harry Randall pass and beat Zack Wimbush to dive into the left corner.
Williams' penalty soon after extended the lead to 10 points and Exeter then had Australia star Tom Hooper forced off with a shoulder injury just before the interval.
Despite that setback, Henry Slade almost dotted down a Sam Wolstenholme grubber kick four minutes after the restart before Exeter's maul got them back into the game soon after.
First the pack earned themselves a penalty and the second maul from the resulting lineout 10 metres out saw Fisilau forced over.
The Chiefs forwards won another penalty inside the 22 with eight minutes left, but superb work from Ibitoye saw the Bears turn the ball over six metres out.
Bristol went straight up the field and a penalty resulting from a high tackle was dispatched well by Williams despite the tough conditions.
And the weather proved to be a distraction for Woodburn soon after as he missed a high kick and was put under pressure by Ibitoye, who was stopped inches from the Exeter line.
But eight phases later Georgian replacement Ivanishvili forced his way over to seal a hard-fought victory.
Bristol director of rugby Pat Lam told BBC Radio Bristol:
"I'm really proud of the boys. We did what we needed to do to win, I felt.
"Some might say it's not pretty, but it's the type of rugby that needed to be played in these conditions.
"We knew earlier in the week it was going to be like this, so we just shone the light on this part of the game that we don't always use.
"This was the part of the game that we had to use, so I'm really pleased the boys got their rewards for it."
Exeter director of rugby Rob Baxter told BBC Radio Devon:
"I thought towards the end there we'd worked our way back into it and we had an opportunity to get something, didn't we?
"Obviously our poorest maul of the game probably was at the end point there when you probably needed to have a real killer maul at that stage.
"We weren't quite as good as we needed to be there, so we have to play away from it and then we lost the ball and then I think really that last period was the kind of errors you just can't afford to have in these conditions - not just handling errors but we gave away penalty error as well which gives a shot at goal.
"We did just make more errors than them over the course of today and tactically they were potentially a little smarter."
Bristol: Jordan; Rees-Zammit, Moroni, Williams, Ibitoye; MacGinty, Randall; Genge, Gwilliam, Chawatama, Rubiolo, Batley, Luatua, Harding (c), Grondona
Replacements: Moody, Woolmore, Halliwell, Caulfield, Owen, Marmion, Bates, Ivanishvili
Exeter: Woodburn; Wimbush, Slade, Butt, Hammersley; Skinner, Wolstenholme; Abuladze, Yeandle, Iosefa-Scott, Hooper, Jenkins (c), E Roots, Vintcent, Fisilau
Replacements: Max Norey, Burger, J Roots, Wilson, James, Varney, Haydon-Wood, Harris
Referee: Karl Dickson