Henry Walker scored twice as Gloucester were made to work hard for victory against an inexperienced Exeter side.
The hooker crossed before Exeter hit back through Josh Hodge's fine solo try and Don Armand's close-range effort.
Walker added his second but the Chiefs led at the break, with the Cherry & Whites retaking the lead through Charlie Chapman's 53rd-minute try.
But Gloucester controlled the game from then on and a late penalty try gave them a bonus-point win.
More to follow.
Gloucester: Carreras; Rees-Zammit, Twelvetrees, Atkinson, May; Barton, Heinz; Rapava-Ruskin, Walker, Balmain, Slater, Alemanno, Reid, Ludlow (capt), Ackermann.
Replacements: Socino, Seville, Ford-Robinson, Clarke, Morgan, Clement, Chapman, Sharples .
Exeter Chiefs: Hodge; Woodburn, John, Baldwin, Cordero; Skinner, Hidalgo-Clyne; Kenny, Yeandle (capt), Street, Lonsdale, Price, Armand, Capstick, Tuima.
Replacements: Taione, Southworth, Petch, Witty, Wrigh, Townsend, Relton, Short.
Referee: Luke Pearce