Italy produced a breathtaking display to hand Ireland a 22-15 defeat on what was Andrea Lo Cicero's 103rd and final appearance for the Azzurri and possibly Brian O'Driscoll's last game in an Irish shirt.
Italy had started this campaign with a 23-18 victory over France and after defeats to Scotland, England and Wales ended it with another deserved win over one of the pre-tournament favourites.
It was Italy's fourth win over the Irish but first in the Six Nations.
"Today we were up against great players like Keith Earls and Brian O'Driscoll, but we've proved that there's no reason we should be envying them," said Italy captain Sergio Parisse.
"This tournament has given us a lot of satisfaction because we've managed to put a lot of other teams under pressure and impose our own game."
Italy have now won twice in the Six Nations for only the second time, the last being in 2007.
Ireland, meanwhile, are in danger of picking up their first ever Six Nations wooden spoon if results elsewhere conspire against them.
Despite an opening win against Wales, coach Declan Kidney fell under pressure after defeats to Scotland and England and then a draw against France last week.
While he kept mum on his future -- his contract is up this year -- Kidney admitted Ireland had simply been outplayed.
"They put us under pressure at setpiece in the first 20 minutes, played good territory and got their points up," said Kidney.
"We managed to get a penalty just before half-time to make it 9-6. Then we lost a little bit of what you might call the chess game early in the second half.
"They had good field position inside our 22 and they stayed there until they got their points.
"Huge credit is due to them. It's a big, big win. Obviously the measure of disappointment for us is mirrored by the joys which I'm sure they've experienced."
Ireland, missing injured fly-half Jonathan Sexton, had the early momentum and Paddy Jackson put the first of his 15 points on the board with a sixth-minute penalty after Leonardo Ghiraldini was whistled for a tackle on Conor Murray.
However the visitors' luck soon ran out in a half which saw several of their players come off injured and iconic centre O'Driscoll sent to the sin-bin.
Ireland went in at the interval 9-6 down and without winger Keith Earls and Luke Marshall, both of whom were injured.
Italy had Ireland on the ropes in the opening few minutes of the second half and were finally rewarded with the only try of the game thanks to Gio Venditti, who squeezed the ball over on the right.
Orquera, from 35 metres out, converted to give Italy a 16-6 lead.
Captain Jamie Heaslip lamented Ireland's failure to score a try, which has now lasted four games.
"In all three games that we've lost, it's been a score or two that's separated us, that's the frustrating thing," said Heaslip.
"We've made too many errors, given free shots at goal, turned over too much easy ball at setpiece or just not converted out own opportunities."
Ireland came fighting back and cut the deficit through two successive Jackson penalties to take the score to 16-12 just before the hour and, with Parisse sin-binned, came close to making the breakthrough after a dominant 20-phase spell in which they finally had to settle for another Jackson penalty.
Parisse returned as a tearful Lo Cicero ended his Italy career to a standing ovation, but Italy spurned another chance to extend their lead when Garcia's penalty effort was short and wide.
When Orquera was restored to kicking duties minutes later he sent Italy 19-15 in front.
It was a key moment for Kidney.
"You get a try then, all of a sudden you're up by a few points," he added. "Unfortunately we lost the lineout, it was our put-in, and we didn't see a lot of the ball for the rest of the game."
Ireland were further penalised when Conor Murray was sin-binned for a tripping offence.
Italy won yet another lineout and a subsequent penalty, with Orquera sealing victory in the final minute.