Hooker Dan Sheehan scored a hat trick to help champions Ireland to a 22-17 bonus-point victory over hosts Italy on Saturday.
While it was the result they needed to keep themselves in with a chance of claiming the title, England's thrashing of Wales ended Ireland's hopes.
It was job done for Ireland with their five-point haul, but as with much of this Six Nations campaign under stand-in coach Simon Easterby, the performance was far from convincing.
Italy were much improved on what has gone before in this campaign and avoided the wooden spoon thanks to Wales poor efforts in Cardiff.
Italy made the game's first score as fly-half Paolo Garbisi's perfect grubber kick sat up for Ioane to gather and cross in the corner.
Ireland prop Finlay Bealham had a try disallowed for a double movement but the visitors did register a first score with a simple backline move from a five-metre scrum that sent Keenan over the tryline.
Italy lost three forwards inside the opening half-hour as lock Dino Lamb, number eight Lorenzo Cannone and flanker Sebastian Negri all limped out of the match.
Tommaso Allan's long-range penalty gave Italy the advantage again, but Ireland led 12-10 at half-time as, after Lamaro's deliberate knock-down at a ruck and subsequent yellow card, the visitors mauled their way over for Sheehan to score.
Ireland camped in the Italy 22 at the start of the second period and were rewarded with a second score that was a carbon copy of their first as Sheehan was at the back of a rolling maul.
Vintcent received a yellow card, later upgraded to a 20-minute red on bunker review, for head-on-head contact with Keenan as the replacement flanker was too upright in the tackle.
Sheehan scored his third try when he collected Mack Hansen's tap-back from a Jamison Gibson-Park kick to complete his hat trick.
Ireland should have been out of sight, but Jack Crowley's three missed conversions kept their hosts in the game.
And when Varney scored Italy's second converted try following a brilliant break from Ange Capuozzo, the gap on the scoreboard was only five points with 18 minutes remaining but Ireland hung on for the win.
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