Tries from Ross Wardle, Hallam Amos and Rynard Landman helped the Dragons to their second league win of the season.
Andrea Manici replied for the visitors, but Lyn Jones’ men secured victory at a wet and windy Rodney Parade.
Tom Prydie fired the Dragons in-front after seven minutes. The hosts had been camped in Zebre territory during the early exchanges and their pressure told when they failed to roll away 20 metres from their line, and Prydie made no mistake.
But Kelly Haimona levelled the scores mid-way through the first-half with a penalty of his own after second-row Andrew Coombs was guilty of making a tackle without his arms.
The Rodney Parade region hit the front moments later through Wardle. Jonathan Evans collected a high Zebre kick and set Prydie free, the full-back raced past the covering Zebre defence and found Wardle with a bungled pass, but the centre managed to pick-up and darted over.
Prydie snatched the chance to give the Dragons a 13-6 lead at half-time after Mauro Bergamasco saw yellow for not rolling away at a ruck.
Leonardo Sarto was the next Zebre man to be sent to the bin for a tip-tackle on Brok Harris, and the Men of Gwent made their two-man advantage count straight away. Wardle and Jack Dixon made inroads into the defence before Jason Tovey fired a miss pass into the arms of Amos who went on to score.
Landman was next over the line for his first try in a Dragons shirt before Zebre drove Manici over for their first five-point score. The Newport region fought-hard, but failed to clinch a try-scoring bonus-point.
