Roberts scored late on to resounding cheers in what was his final appearance at his hometown ground before moving to France next season.
It completed a resounding victory for the Blues that defied the heavy conditions and clinched qualification for next season’s Heineken Cup.
Rhys Patchell and Gavin Evans also crossed while Leigh Halfpenny kicked 13 points to regain eighth place in the Pro12.
Cardiff were rewarded for their ambition on a muddy surface when Patchell burst over on 18 minutes.
Michael Paterson stole a Zebre lineout five yards from their try line and the 19-year-old fly-half squeezed between two defenders before carrying another pair over the line.
Halfpenny converted and traded further penalties with Daniel Halangahu for a 16-6 lead before Patchell sparked his team’s second try.
He skipped out of defence past a cynical trip that earned Zebre wing Leonardo Sarto a yellow card.
Patchell continued forward to find Roberts before Evans had the legs to race over from 30 metres out for a 21-6 lead at half-time.
The second half was played almost entirely in Zebre territory but it was not until the 72nd minute that Cardiff finally got the third try.
Patchell was narrowly wide with a drop goal, Roberts went within inches of scoring and Owen Williams was twice put clear by his team-mates.
Finally came the try that almost 10,000 Blues fans had come to see as Roberts bounced his way through several Zebre tacklers to cross.
Filippo Cristiano dived over in the final seconds for Zebre but even that could not spoil the post-match farewell for Roberts and Exeter-bound pair Ceri Sweeney and Tom James.
