Wing Giovanbattista Venditti's 49th minute try, 14 points from flyhalf Luciano Orqeura and a penalty to centre Gonzalo Garcia were enough to stop a lacklustre Ireland side, who had to rely on the boot of flyhalf Paddy Jackson for all their points.
Ireland were penalised for their indiscipline by losing Brian O'Driscoll, Donnacha Ryan and Conor Murray to the sin bin.
Italy ended the championship with two wins after defeating France in the opening round. They finished ahead of Ireland who lost three games and drew one after upsetting last year's grand slam champions Wales on the first day of the tournament.
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