Tries from fly-half Rhys Patchell, and centres Gavin Evans and Jamie Roberts, coupled with two conversions and three penalties for a 13-point haul from RBS 6 Nations player of the tournament Leigh Halfpenny were enough to beat the Italian outfit.
Bottom of the table Zebre are still searching for their first win in the league since being formed last summer but never looked likely to upset the Blues.
It was the Welsh region's final home match of the campaign but the conditions meant it was near impossible to give the departing Roberts and Ceri Sweeney a Barbarian style send-off of running rugby.
Lions and Wales centre star Roberts is joining French big spenders Racing Metro while former Wales fly-half Sweeney has signed for Exeter Chiefs.
Roberts crashed over for his touchdown late on as the Blues overtook Connacht who had passed them in the standings on Friday night courtesy of a win over Edinburgh.
It was only the Blues' third triumph of the league programme at the Arms Park following their move back from the Cardiff City Stadium.
Zebre were game opponents but lacked the skill, power, pace and confidence to provide a serious challenge. Their only try, from substitute Filippo Cristiano, came in the final minute.
Former New South Wales Waratahs Super 15 ace Daniel Halangahu had given them a three-point lead with a penalty in the second minute after the Blues infringed at a ruck.
Halfpenny punished Zebre in the 11th minute by levelling matters with a straightforward penalty after a Zebre tackler failed to release his victim.
They took the lead when back-row forward Michael Paterson picked off an opposition hooker Davide Giazzon's throw at a line-out for Patchell to squirm his way over for Halfpenny to convert.
Blues began to assert their authority and the pressure they generated resulted in Halfpenny making it 13-3 in their favour with another not too demanding penalty,
Zebre had a chance when Patchell was driven back over his try-line after attempting to tidy up a loose pass but they coughed up possession following the five metre scrum.
Nevertheless, they managed to stay in Blues' territory with Halangahu cutting the deficit to four points with his second successful penalty. Again, it came from an offence at a breakdown.
Halfpenny restored a 10-point advantage for the Blues with a trademark long-range penalty strike after Giazzon failed to release after being tackled.
And it got better on the stroke of half-time when Patchell counter-attacked from deep and found Evans just inside a touchline.
The centre accelerated and out-sprinted the cover for a runaway try to make it 21-6 in favour of the Blues.
Zebre had right-wing Leonardo Sarto sin-binned for attempting to trip Patchell while Halangahu was short with a long-range penalty attempt.
A magnificent leap and catch from Roberts when he chased an up-and-under from Halfpenny led to the Blues securing a penalty.
They turned down a kick at goal and went for a try. Roberts was stopped just short of the line after sliding forward while right wing Owen Williams was bundled into touch near a corner flag.
Roberts eventually got over, Halfpenny adding the conversion, before Cristiano replied with a try converted by fellow replacement Alberto Chiesa.