With eight minutes remaining, Callum Sheedy succeeded with a touchline conversion to Naulago’s third to give Bristol a 24-23 bonus-point victory and condemn Worcester to an 11th successive defeat.
Andy Uren was Bristol’s other try-scorer with Sheedy kicking two conversions.
Perry Humphreys and Francois Venter scored Worcester’s tries with Billy Searle kicking three penalties and a conversion. Jamie Shillcock added a conversion.
Worcester suffered a pre-match blow when their captain Ted Hill was forced to withdraw, having failed to recover from a back problem.
Bristol began strongly to take a fifth-minute lead. From a line-out on the Warriors’ 22, Bears secured possession for Sheedy to throw out a superb long pass to Naulago, who had an unopposed run-in.
The hosts conceded five penalties in the first 12 minutes but they slowly grew into the game to make it an evenly contested first quarter.
Naulago’s try was the only score in that period but the wing should have had a second but Henry Purdy sent out a poor pass with the try-line in sight.
However Naulago was not to be denied when a strong run from Niyi Adeolokun put the defence on the back foot before Sheedy fired across a well-judged cross-field kick for the Fijian to collect and score.
Worcester suffered another setback when Chris Ashton, making his home debut, was forced to leave the field for a head injury assessment with Searle replacing him.
The former Bristol man immediately made an impact when his cross-field kick provided Humphreys with a simple pick-up to score. Shillcock converted before Searle brought the scores level with a penalty.
Warriors could have taken the lead when another replacement, Ashley Beck, intercepted Sheedy’s pass to run 50 metres but the Welsh centre was hauled down 10 metres short of the line.
It proved crucial as Bears regained the lead when Uren dashed over from close range with Sheedy’s conversion giving his side a 17-10 interval advantage.
Five minutes after the restart, Searle reduced the arrears with a penalty before Worcester took the lead for the first time with a brilliant team try with excellent handling resulting in Venter scoring.
Searle converted before kicking a penalty and Worcester looked set to pull off a shock victory but with Bears’ nerves jangling, Naulago powered away for his hat-trick with Sheedy coolly converting from the touchline to secure victory.