Steve Tandy's side scored three tries at the Stadio XXV Aprile, with fly-half Dan Biggar claiming 24 points.
He opened the proceedings with a sixth-minute penalty and, after Gonzalo Garcia had levelled, he pushed his side out to 9-3 with two more three-pointers.
Zebre's Alberto Chillon was then sent to the sin-bin and Richard Fussell made the most of his absence by grabbing his side's first try.
Biggar converted and, when Jonathan Thomas went in as well, the Ospreys led 21-6 at the break, with Daniel Halangahu scoring a penalty on the whistle.
Luca Redolfini then touched down (43) and when Halangahu converted it was 21-13, before he and Biggar traded penalties.
The Scotland international would have the last word, though, scoring a fifth penalty before converting his own try inside the last quarter.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.