The hosts made a positive start to the contest and were ahead inside three minutes when Greig Laidlaw split the sticks to open the scoring.
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It was Gloucester who took control before the interval, though, with Laidlaw adding two more successful penalties to his personal tally, in between Stephen McColl's try which followed some fine handling by the returning Billy Twelvetrees.
James Hook further strengthened the Aviva Premiership outfit's advantage when he burst through, capitalising on phases breaking down the Zebre line.
Michele Visentin touched down on the overlap six minutes after the interval to give the Italian club a glimmer of hope, but Gloucester well and truly made sure of the points with two more tries late on.