After disappointing defeats at Cornish Pirates and Bedford, Carnegie put in a performance of huge commitment to impress their newly-appointed director of rugby, Chris Stirling, and led 13-12 with 10 minutes left on the clock.
However, two penalties from Ian Madigan and a yellow card for Carnegie captain Richard Mayhew allowed the leaders to escape with the spoils.
After surprisingly losing their unbeaten record to Jersey in their last home fixture, an explosive start was expected from the hosts but Carnegie matched them before a Madigan penalty put Bristol ahead.
Joe Buckle limped off as both sides struggled to bring any continuity to their game with frequent handling errors ensuring that the try-line went unthreatened.
A powerful burst from Bristol skipper Jordan Crane brought some much needed excitement and when the visitors were penalised, Madigan extended the lead with a simple kick
Carnegie continued to infringe and conceded a third penalty success to Madigan before Callum Irvine put them on the scoreboard with the last kick of the half.
Three minutes after the restart, home prop Gaston Cortes was sin-binned for collapsing a scrum as Carnegie maintained their dominance in that area but they suffered a setback when prop Marc Thomas was stretchered from the field with a leg injury.
The visitors failed to capitalise on the absence of Cortes until they were awarded a penalty try as Bristol’s scrum again folded.
Madigan’s fourth penalty put Bristol back in front. With 13 minutes remaining, a further scrum penalty and subsequent back chat to concede 10 metres saw Irvine succeed with his second penalty but those two late penalties from Madigan saw Bristol to a fortunate win.
Bristol : Morahan, Edwards, Piutau 6 (J.Williams 40), Pisi, Leiua, Madigan, R.Williams (Uren 78), Bevington (Tonga’uiha 40), Harris-Wright (Fenton-Wells 69), Cortes (Lay 54-72,), Joyce, Latta (Jeffries 19), Haining, Crane, Thomas.
Carnegie: Elder, Watkins, Forsyth, Lucock, McColl, Irvine, Fox (Elliott 75), Thomas (Thraves 51), Buckell (M. Mayhew 25), Mitchell (Bryce 59), Whetton, Smith (Bainbridge 59), West, Beck, R. Mayhew.