Northampton Saints slumped to a third defeat in four as Bath won at The Rec, while Wasps and Bristol also secured victories.
Charlie Sharples grabbed two tries as Gloucester rallied from a 10-point half-time deficit to see off local rivals Bristol Bears.
Danny Cipriani inspired Gloucester's comeback as a former Bath player denied the hosts victory at the Rec on Saturday.
The opening game of the 2018-19 Premiership season saw newly promoted Bristol Bears defeat Bath 17-10 in a lively west-country derby.
Tom Varndell has swapped the Championship for the Pro14 after agreeing to leave Bristol for Scarlets.