Ian Whitten, Dan Tuohy and Craig Gilroy crossed for the visitors' three tries at Stadio Luigi Zaffanella, while Ian Humphreys added two penalties and two conversions.
Former Munster player Nick Williams scored the Italians' only try with Naas Olivier kicking 14 points.
Ulster started strongly and a Whitten score and a converted Tuohy try either side of an Olivier penalty had the Irish side 12-3 in front.
Aironi, though, came back into the match as another Olivier penalty and a converted try from New Zealander Williams put them 13-12 in front.
They would not hold out until half-time, though, as Humphrey kicked a long-range penalty to give Ulster a 15-13 interval lead.
Olivier then kicked the hosts back in front, but Gilroy scrambled over for a crucial third try for Ulster and Humphreys added the extras to give them a 22-16 advantage.
Humphreys took his personal haul to 10 points with his second penalty to give Ulster a cushion, and even though Olivier struck another penalty, this time Aironi could not mount a fightback.
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.
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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.