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.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
