Ireland had slim hopes of an historic third consecutive title, and the unconvincing bonus-point win in Rome was overtaken as expected within hours by England, who finished second, and France, the new champion.
A week after Ireland were hammered by France in Dublin and lost control of their destiny, they briefly regained the tournament lead with a fourth win in five matches.
But the Triple Crown holders suffered a French hangover trying to force too much against an Italy determined to show their best side after conceding 18 tries to France and England.
"There's a little bit of disappointment that we didn't play at our best," Ireland interim coach Simon Easterby said.
"Credit to Italy, they had a part to play in that. We coughed up too much possession and didn't make the most of some opportunities."
The Irish scored four tries to two and enjoyed 30-plus minutes with a man advantage, but a clunky, deflated performance gave Italy hope of an upset.
Italy frequently found holes in the Irish defence but three yellow cards - one of them turning into a 20-minute red - undid all of their impressive work.
The highlight of Ireland's display was hooker Dan Sheehan's first Test hat-trick of tries, extending his men's Six Nations record for a forward to 13.
Sheehan scored his third try when he collected Australian Mack Hansen's tap-back from a Jamison Gibson-Park kick to complete his hat-trick.
Fullback Hugo Keenan could have had a hat-trick, too, but one was ruled out and another wasn't given.
Italy played for half an hour with 14 players after yellow cards for Michele Lamaro and Giacomo Nicotera, and a 20-minute red for Ross Vintcent, but managed tries through Australian winger Monty Ioane and scrum-half Stephen Varney in a spirited end to their campaign.
"Relief is the overriding feeling," Ireland captain Caelan Doris admitted afterwards.
"It was a proper battle that went down to the wire.''
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