The hosts led 23-0 after a dominant first-half display, with Henry Purdy, Ross Moriarty and Steve McColl all crossing and Billy Burns kicking a conversion and two penalties.
Zebre were later awarded a penalty try which Edoardo Padovani converted.
Padovani also slotted a penalty for the Italian side while Gloucester failed to earn a four-try bonus point win.
Purdy went over in the corner, Moriarty bundled over and McColl outpaced the Zebre defence to score three unanswered first-half tries.
Gloucester lost Lewis Ludlow to the sin bin early in the second half and Zebre were awarded a penalty try as they reduced the deficit.
Henry Trinder made his comeback from injury but he failed to help his side earn the extra point a fourth try would have sealed, with a Padovani penalty completing the second-half scoring.
Gloucester head coach David Humphreys told BBC Radio Gloucestershire:
"We got a win in difficult conditions and I was very pleased with the performance of some of the players who came in.
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"What makes the second half even more disappointing was that the first half was so good.
"We just never really got going, error after error, penalty after penalty, and once than happens sometimes it's hard to change the momentum in a game.
"We have got to develop a squad that has 30 players ready to come in and play, make a change here, rest a player here, and the performance doesn't suffer."
Gloucester: Cook; McColl, Meakes, Atkinson, Purdy; Burns, Braley; Thomas, Lindsay, Doran-Jones; Stooke, Thrush; Moriarty, Rowan (capt), Ludlow.
Replacements: Dawidiuk, Murphy, Thomas, Hicks, Thomas, Laidlaw, Trinder, Thorley.
Zebre: Palazzani, Berryman, Bisegni, Pratichetti, Sarto, Padovani, Violi, Lovotti, D'Apice, Chistolini, Bernabo, Bortolami (capt), Sarto, Meyer, Ferrarini.
Replacements: Fabiani, de Marchi, Ceccarelli, Biagi, Caffini, Burgess, Toniolatti, Canna.
Referee: Andy Brace (Ireland).
Attendance: 9,973
European Challenge Cup holders Gloucester got their defence under way with a comfortable victory over Zebre.