But their win came at a cost with potentially devastating hamstring injuries to centres Brian O'Driscoll and his Leinster teammate Gordon D'Arcy.
Both men now face a battle to be fit for next Saturday's clash with Scotland.
"Gordon isn't good and I think will be under pressure for next weekend. It doesn't look great for Brian," said Ireland coach Eddie O'Sullivan.
"He was tired as well so it's hard to know how much damage there is."
Ireland, looking to win the tournament for the first time since 1985, scored three tries through Geordan Murphy, Peter Stringer and Denis Hickie, while Ronan O'Gara added 13 points with his boot.
Leandro Castrogiovanni scored a late try for Italy to add to their four penalties. Ronald De Marigny converted three of them and Luciano Orquera the other.
The home side might have even ran the tournament favourites closer had they not missed three penalties and Ludovico Nitoglia not been denied a try by referee Paddy O'Brien, who ruled the Calvisano wing didn't have control of the ball when he touched down in the second half.
O'Sullivan admitted his team were lucky to escape with a victory.
"I would have to say Italy played really well and that if we had lost that game today we couldn't have had too many complaints," he said.
"They matched us all the way and if they had been more accurate with their kicking things could have been very different. It just goes to show that anything can happen on the day in this tournament."
Italy coach John Kirwan was full of pride for his team having seen them produce one of their best performances since joining the tournament in 2000.
"The result is not important, it's more about the performance," said the former All Black.
"I can't criticise the players as we matched the Irish all the way and could have done something when Ludovico scored what we thought was a try.
"It was an important experience and now we have to take all the positives from this match and get our minds fixed on playing Wales next week."
Italy started brightly in front an expectant home crowd and struck the first blow in the eighth minute when Petrarca Padova fly-half Orquera made up for an earlier miss by slotting a penalty from just outside the 22-yard line.
More Italy pressure failed to translate into points and Ireland drew level in the 22nd minute when indiscipline cost the home side a penalty underneath the posts which O'Gara converted with ease.
Having woken from their early slumber, Ireland maintained the momentum, scoring the first try in the 25th minute. In a blur of movement, O'Driscoll swerved past three tackles before feeding Murphy, who touched down in the corner. O'Gara failed to add the conversion.
Ireland suffered a major blow moments later when D'Arcy hobbled off injured and was replaced by Girvan Dempsey.
After missing another penalty, Orquera handed the responsibility to De Marigny for the next kick and the Overmach Parma full-back did not disappoint, pulling Italy to within two points of the visitors at half-time with a long-range effort.
South African-born De Marigny put Italy 9-8 ahead soon after the break with another confident penalty which significanlty raised the level of noise from the home supporters, but their joy was short-lived as the Irish responded in style with a superb try.
O'Driscoll broke down the left wing before releasing Hickie, who quickly off-loaded to Shane Horgan. With his back to play, the Leinster wing threw the ball over his head to Stringer who went over in the corner.
O'Gara converted before drilling another penalty to give Ireland a 18-9 lead.
Italy who have won three games since their inclusion in the northern hemisphere tournament five years ago, refused to lie down and another De Marigny penalty reduced the deficit to six points on the hour.
The hosts thought they had scored a try when Nitoglia took advantage of some poor Irish handling, but after consulting the video O'Brien ruled out his valiant effort.
Another O'Gara penalty was followed by a splendid Hickie try after good work from O'Driscoll and O'Gara's conversion made it 28-12 to the Irish.
Castrogiovanni ensured the game ended on a high note for a gallant Italy side, breaking through some weak Irish tackling for his side's only try, while the Irish were rocked by the sight of O'Driscoll being carried off the pitch.
Italy: 17 Tries: Castrogiovanni Pens: Orquera, De Marigny 3
Ireland: 28 Tries: Murphy, Stringer, Hickie Cons: O'Gara 2 Pens: O'Gara 3
De Marigny; Mi Bergamasco, Canale, Masi, Nitoglia; Orquera, Troncon; Lo Cicero, Ongaro, Castrogiovanni; Dellape, Bortolami; Persico, Ma Bergamasco, Parisse.
Replacements: Perugini, Intoppa, Del Fava, Dal Maso, Griffen, Pozzebon, Robertson.
Murphy, Horgan, O'Driscoll, D'Arcy, Hickie, O'Gara, Stringer, Corrigan, Byrne, Hayes, O'Kelly, O'Connell, S Easterby, Leamy, Foley.
Replacements: Sheahan, Horan, O'Callaghan, Miller, G Easterby, Humphreys, Dempsey.
Referee: P O'Brien (New Zealand)