The stand-off Paul Burke landed two penalty goals inside the first nine minutes to give Ireland a solid start, but from then on the Italians, who England play in the opening stages in South Africa, had the edge in virtually every aspect of the game.
Italy's talented stand-off Diego Dominguez levelled the scores with two well-taken penalties but five minutes before the break Burke put Ireland back in front with another penalty.
Dominguez dropped a fine goal to put Italy level, but the see-saw contest continued when Burke's fourth penalty goal gave Ireland a 12-9 interval lead.
The second period was dominated by Italy and Dominguez knocked over another penalty to tie the scores 10 minutes after the break.
Then an excellent attacking move saw the full-back Paulo Vaccari go over for an superb try which Dominquez converted. Ten minutes before the end, Dominguez landed his fourth penalty to seal victory.
In Sydney Australia fought back against a spirited Argentina for a face- saving 30-13 victory in the second Test, taking the series 2-0.
The Pumas looked set for a surprise win after the World Cup holders failed to exert the same dominance that swept them to a 53-7 win in the first Test in Brisbane last weekend.
The tourists, who managed only one provincial win, showed a complete reversal of form, driving the Wallaby pack backwards in the scrums and repelling back-line attacks with solid defence.
In wet, cold conditions before a crowd of around 28,000, the Pumas played much of the first half inside the Wallabies' territory, with the replacement full-back Lisandro Arbuzi scoring the game's first try just before the break.
Argentina led 13-3 going into the second half, but were eventually overhauled after the wing David Campese ran in two tries to take take his world record tally to 63.Reuse content