The Dragons have managed a losing bonus point despite a defeat by Leinster at Rodney Parade in the Pro12.
The home side initially led 10-6 half time with a try by Ross Wardle, but were behind for much of the game.
However they put in a brave fightback to eventually go down by a respectable 23 points to 19.
Ospreys flanker Justic Tipuric scored a try in each half to help his Ospreys side to a 40-17 win over the Dragons. The visitors got off to a good start, with Tom Prydie scoring in the corner after only four minutes.
It did not take the home side long to respond, though, as Dan Biggar made the most of a penalty to put three points on the board for the Ospreys.
There was concern for Wales No. 8 Toby Faletau, who was stretchered off with a head and neck injury.
Newport Gwent Dragons have opened their Amlin Challenge Cup campaign with a win over Mogliano.
The Dragons face Italian side in the PRO12 at Rodney Parade tonight.
The Newport side have made a promising start to the season under new director of rugby Lyn Jones, with victories against Ulster and the Scarlets, but defeat to Munster and Edinburgh.
Zebre claimed their first win since being formed, with a thrilling 30-25 victory over Cardiff Blues a fortnight ago.
The Italian side were founded in 2012, and lost every match in their debut PRO12 season.
Lions No8 Toby Faletau is back in the Dragons' line-up, one of several changes in the forwards.
Second row Rob Sidoli, who makes his first start of the season, said: Zebre have "improved a lot. I think that they are a genuine threat as they had a really good result against the Blues which was away for them."
"They have some really good individuals and their core basics are very strong; they will have a good driving line outs and scrum so those are the things we need to get up to speed on quite quick.”
The Dragons started their PRO12 season with a morale-boosting win over Ulster at Rodney Parade.
Returning fly-half Jason Tovey kicked four penalties and a drop goal for the hosts.
Their Irish opponents topped the league last year, only missing out on the PRO12 title in the final against Leinster.
Newport Gwent Dragons have extended the contract of Wales and British and Irish Lions Number 8 Toby Faletau for two years, in a deal that will see him stay with the region until 2016.
"Throughout discussions with Toby I have been extremely impressed with his drive and motivation not only on a personal level but in his commitment to developing the Dragons into the best team in Wales" said Lyn Jones, Dragons Director of Rugby.
The Dragons have confirmed that Lyn Jones will be their new director of rugby.
The 49-year-old left his position as head coach of London Welsh last week, saying he wanted to return to Wales to be closer to his family.
He has previously coached the Ospreys, and worked as a consultant with the Dragons in 2009.
Darren Edwards will stay at Rodney Parade as head coach, with Robert Beale moving from rugby director to team manager.
Dragons chairman Martyn Hazell said: "Last season was a difficult one for us at the region, but having brought our finances under control, we are looking to build our team for the future."
"With some key signings made during the off-season, we are confident that Lyn has the experience and expertise to support our coaching team and ensure that we get the very best out of our group of young, talented players."
Former Wales international rugby player Matthew J Watkins has announced he has cancer.
He says he has a very rare form of cancer of his right pelvis, but "remains well and active" while being treated at Velindre Cancer Centre in Cardiff.
“Obviously it’s very disappointing news for me and my family but I’m keen to progress with my treatment and battle the illness with the same commitment as I gave to my rugby career", he said.
“I would like to thank everyone who has offered their support and the fantastic support from the guys at Velindre Cardiff. I am determined to continue my everyday life with my family and friends."
The Dragons have secured victory against Munster by a six-point margin.
The Ospreys stormed to victory tonight with a magnificent 52-19 win over the Dragons.
Tries by Dan Evans and Toby Faletau for the Dragons could not match the assured performance of their hosts.
Ospreys' number seven Justin Tipuric scored try number seven for his side.