Ireland produced a superb display of running rugby to give themselves an excellent chance of securing their first Six Nations title since 1985.
France must now beat Scotland in Paris by 24 points or more to take the title.
First-half tries by Girvan Dempsey, Simon Easterby and Gordon D'Arcy gave Ireland a 20-12 lead after a hard-fought first half.
But four tries in a 13-minute period after the break from Dempsey, Shane Horgan, Denis Hickie and Ronan O'Gara opened up the game.
Italy grabbed two consolation tries in the closing 10 minutes through captain Marco Bortolami and fullback Roland De Marigny.
Man-of-the match D'Arcy was the architect of most of Ireland's good work and he needed to be at his very best to dig Ireland out a difficult first half that saw the Italian forwards dominate the scrums and line outs.
Italy were well in touch in the first half thanks to the left boot of fly-half Pez. After O'Gara opened with a penalty, Pez levelled with a drop-goal and then added a penalty to give Italy a 6-3 lead.
Dempsey then got the opening try in the left corner after good build-up involving D'Arcy and Brian O'Driscoll with 16 minutes played.
Five minutes later Horgan set up Llanelli flanker Easterby for Ireland's second try.
Another penalty and drop goal from Pez reduced the deficit to just one point before Ireland scored a controversial third try just before the break.
Hickie's scoring pass to D'Arcy was clearly forward but the Leinster centre was allowed to go on and score.
Four tries after the break then saw Ireland pull away. First, Dempsey charged through a large gap and over the line, with O'Gara adding the conversion.
Ireland then ran in their fifth try with Hickie carving through Italy's midfield and picking out Horgan, who raced home unchallenged.
Hickie crossed himself following a superb dummy and then O'Gara touched down, chasing a kick after D'Arcy had broken from his own half.
Skipper O'Driscoll was heavilly involved in the score but was forced to leave the field with an ankle injury.
Bortolami scored Italy's first try in the 74th minute after gathering a high cross-field kick, but Hickie re-established Ireland's lead with his second try of the game.
However, a stoppage-time touchdown by de Marigny, which had to go to the video referee, took some gloss off the Irish triumph.