The hosts had led 14-6, Colin Wilkie scoring two tries with Terry Campese converting both and kicking a penalty.
Anthony Walker's try just before half time brought Wales back into the match with Andrew Gay edging them ahead before Ben Morris' second decisive try.
"I'm glad we've got there and it does give impetus to the work that is going on in Wales," said coach John Kear.
"I was absolutely delighted.  I'm really pleased with what the players demonstrated in the second-half with regards to the collective spirit, unity and determination.
"There's no doubts they fully deserved that. It was tough to come here. We've played an Italy team of which 15 of the 17 are heritage players - Australian-based.
"It's been a tough old afternoon, but it's been a rewarding afternoon."
Wales have qualified for the 2017 Rugby League World Cup after coming from behind to beat Italy in Monza.