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.