It took 28 minutes for the deadlock to be broken at Stadio Sergio Lanfranchi, in-form wing Owen Lane taking an offload from Rey Lee-Lo before racing away to go under the posts and Jarrod Evans adding the extras.
Zebre have claimed only four victories in Conference A, but they were level when Giovanbattista Venditti intercepted a loose pass to dart away for a try four minutes before half-time.
Guglielmo Palazzani converted to level the contest, but Evans was on target with a penalty just before the break to edge Cardiff back in front.
Zebre applied the pressure without reward in a scoreless second half in Parma, Cardiff clinging on to move six points behind the third-placed Cheetahs.
WOW! ?Giovanbattista Venditti intercepts the ball and runs the length of the field to cross the whitewash for @ZebreRugby just before half-time! ?
— PRO14 RUGBY (@PRO14Official) February 25, 2018
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