The Cherry and Whites looked all set for a decisive second-round win when they led by 19 points with only 15 minutes left at Ashton Gate.
But three Bristol tries in rapid succession levelled the scores before Gloucester full-back George Barton kept his cool when on target with a 78th-minute penalty.
Wade threatened to go from hero to villain when he was yellow-carded late-on but Gloucester survived one last Bristol surge.
Earlier, Wade -- back in the Premiership after six years away in the NFL and a spell with Paris-based club Racing 92, demonstrated he had lost none of his finishing skill.
The 33-year-old's treble took Wade to 85 Premiership career tries, putting him equal fourth with former England scrum-half Danny Care on the all-time list.
Gloucester lock Freddie Thomas and fly-half Gareth Anscombe also went over for Gloucester, with Barton converting all five tries and landing three penalties for a 19-point haul.
Bristol's Max Malins (two), Siva Naulago, Harry Randall, Gabriel Ibitoye and Rich Lane all scored tries -- and AJ MacGinty kicked 11 points -- but their efforts could not deny Gloucester.
