The bonus-point win ensured that Quins only have to secure one point from their remaining two games to top Pool Three and hopefully secure a home draw in the quarter-finals.
Quins took some time to subdue the visitors but once Zebre picked up two yellow cards in quick succession, it was a case of damage limitation as the home side scored seven tries and collected 18 points from the boot of Nick Evans.
Tom Casson, Ben Botica, Nick Easter, Sam Smith, Danny Care and Karl Dickson crossed for Quins, who were also awarded a penalty try. Ruggero Trevisan scored Zebre's only try of the game.
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