Italy beat Ireland for the first time in Six Nations history in what may prove to be iconic centre Brian O'Driscoll's last game for the Irish.
O'Driscoll, 34, was also yellow carded for a stamp in the first half.
Italy led 9-6 at the break and extended their advantage through Gio Venditti's converted try.
Paddy Jackson landed three quick penalties but Luciano Orquera's brace of penalties gave Italy two wins in the Championship for only the second time.
Their only previous win double came in 2007, while Ireland's fourth Six Nations game without a win is their worst run in the Championship since it increased from five to six teams in 2000.
Ireland also lost three men to injury in the first half and had three men sent to the sin bin, and they will end up with the Wooden Spoon if France beat Scotland by 17 points in the final match of the Championship.
Italy were the better team throughout, with their pack dominating at the line-out and around the park, and if they had more of a cutting edge would have ensured their fans would have been able to relax far earlier than the final 10 seconds of the match.
Captain Sergio Parisse, back-row colleague Alessandro Zanni and hooker Leonardo Ghiraldini were all outstanding as the Azzurri backed up their fine win over France on the opening weekend.
Ireland fly-half Jackson, who went into the game with a kicking accuracy of only 42%, drilled over an early penalty to settle his nerves and get the scoreboard ticking over.
But Italy, with Parisse once again a real threat with ball in hand, won three quick penalties of their own.
Fly-half Orquera clipped over two from three - hitting the post with the middle attempt - to give Italy a 6-3 lead after 21 minutes, and things soon went from bad to worse for Ireland.
The visitors, who had gone into the game missing 13 players through injury, lost Keith Earls and Luke Marshall to injury in quick succession.
They also saw Jackson miss a penalty before the moment of madness from O'Driscoll.
The Irish great, normally so controlled in his play, stamped on Italy flanker Simone Favaro at a ruck and was sent to the sin bin.
With the Championship's all-time leading try-scorer off the pitch, Italy tried to hammer their advantage home but could only manage a third penalty, banged over from distance by long-range kicker Gonzalo Garcia.
Astonishingly, Ireland then lost a third man to injury as Luke Fitzgerald was forced off, with 21-year-old Iain Henderson coming on at blind-side flanker and Peter O'Mahony moving to the wing.
But they were given a glimmer of hope as Jackson landed his second penalty in the last action of the half to make it 9-6 at the break.
The visitors were lucky to be within three points and Italy finally made their dominance count as winger Venditti capped his fine tournament with a powerful drive from short-range.
Orqeura drilled the conversion from wide on the right and it looked as though Italy were sitting pretty, but with just under half an hour to play, home captain Parisse was yellow-carded for a trip on Ian Madigan.
During the number eight's absence Jackson landed three penalties - including one that came after a 20-phase attack that was finally halted two yards from the Italy line - to cut the lead to one point and set up a nerve-wracking finale.
Garcia missed a long-range penalty that would have given the hosts a little more breathing space but Donnacha Ryan was sin-binned for a late tackle and Orquera made no mistake with the penalty.
The visitors then lost a third man to the sin-bin, scrum-half Conor Murray yellow-carded for a trip, and Orquera's last-gasp penalty wrapped up a historic win for the hosts.
Italy: Masi; Venditti, G Canale, Garcia, McLean; Orquera, Gori; Lo Cicero, Ghiraldini, Cittadini, Geldenhuys, Furno, Zanni, Favaro, Parisse.
Replacements: Benvenuti for Masi (66), Botes for Gori (75), Rizzo for Lo Cicero (64), Giazzon for Ghiraldini (75), De Marchi for Cittadini (75), Pavanello for Geldenhuys (64), Minto for Furno (58), Derbyshire for Favaro (58).
Sin Bin: Parisse (52).
Ireland: Kearney; Gilroy, O'Driscoll, L Marshall, Earls; Jackson, Murray, Healy, Best, Ross, McCarthy, Ryan, O'Mahony, O'Brien, Heaslip, Fitzgerald.
Replacements: Madigan for L. Marshall (28), Fitzgerald for Earls (25), Kilcoyne for Healy (71), Cronin for Best (71), Archer for Ross (67), Toner for McCarthy (64), P. Marshall for Ryan (79), Henderson for Fitzgerald (37).
Sin Bin: O'Driscoll (30), Murray (79).
Ref: Wayne Barnes (RFU).