Danny Wilson’s side led 18-11 at half-time thanks to tries from Blaine Scully and Matthew Morgan but the encounter disintegrated in the second-half despite a Tom James score.
Zebre disrupted any flow and set up a tense finale when Giulio Bisegni crossed but despite failing to convert a number of chances, the Blues closed the game out to go second in the Guinness PRO12.
Wales’ Capital Region went into the encounter on the back of three consecutive wins in the PRO12 and knew a victory at Stadio Lanfranchi could take them to the summit of the league table.
But there was no complacency within the squad following two defeats in their last three visits to Parma.
Wilson made six changes to his starting line-up with Scully coming in for the injured Alex Cuthbert and Steve Shingler getting the nod ahead of Gareth Anscombe.
Rhys Gill, Matthew Rees and Scott Andrews formed a new look front row and Nick Williams returned to number eight.
It took Zebre just three minutes to boot the scoreboard into action after Steven Shingler was penalised for holding on at the breakdown.
The Blues were struggling to get out of their half and both teams were erroneous in the opening minutes but a Matthew Morgan counter-attack laid the platform for Shingler to level the scores.
A rampaging rolling maul, which went more than 30 metres, put the Blues on the back foot and earned the hosts a penalty, which was kicked to the corner.
The following line-out launched another driving maul and although they were held at bay they soon managed to power over with Guglielmo Palazzani the scorer.
Shingler fired a pair of penalties narrowly wide as the pack began to establish a dominant platform at scrum-time.
But the fly-half maintained his composure and bisected the posts on 22 minutes to cut the deficit to two points.
The hosts were dealt a blow when hooker Oliviero Fabiani was sent to the sin-bin on 26 minutes and the Blues immediately took advantage.
They kicked to the corner and went through three phases before Scully ran a razor-sharp line to take a short ball from Lloyd Williams and score underneath the posts.
Shingler knocked over the simple conversion to open up a 13-8 lead, but it was the Blues who fell foul of referee David Wilkinson next, with Josh Turnbull shown yellow for an indiscretion at the breakdown.
But Wilson’s men were undeterred and went through multiple phases, displaying remarkable ball retention before Cory Allen unlocked the Italian defence with a perfectly waited grubber-kick, which was collected by Morgan, who touched down for his first try in Cardiff Blues colours.
Zebre rallied in the closing stages of the half but the Cardiff Blues defence held firm and the hosts were forced to settle for a Carlo Canna penalty.
The Blues made a perfect start to the second-half as Blaine Scully won the restart and Federico Ruzza strayed offside but Shingler fired wide.
Two minutes later Ruzza was penalised again, this time for failing to roll away, and duly sent to the bin.
Gareth Anscombe entered the fray on 45 minutes later and Cardiff Blues quickly added a third try.
Rey Lee-Lo made good yards through the middle and a clever box-kick from Williams set alarm bells ringing.
Zebre collected, as the bounce defied James, but he stripped the ball out of contact and caught the hosts off guard to race into the corner.
Anscombe was unable to convert and the Blues were dealt a set-back when Wilkinson lost patience and sent Rhys Gill to the sin-bin.
The Italian outfit piled on the pressure as the Blues were reduced to 14-men and they eventually broke through with Canna firing a long pass to Giulio Bisegni, who crashed into the corner despite the best efforts of Morgan.
Bisegni’s try set up a tense finale but there were still opportunities aplenty with Lee-Lo prominent.
First he hacked on a clever Anscombe grubber and he was then put in space after the Blues snatched a home lineout.
But with a fourth-try within reach, he was unable to find Scully on the outside as a gilt-edged chance went begging.
Zebre responded and while the Blues defence was resolute, they shot themselves in the foot as Nick Williams knocked on close to his own line.
The hosts pounced and despite a desperate scramble the ball was worked to Giovanbattista Venditti, who squeezed in the corner.
Edoardo Padovani hooked the conversion as a nail-biting finale ensued but the Blues clung onto a two-point lead to draw level with Ulster at the top of the PRO12 table.