Six Nations minnows Italy produced a breathtaking display to hand Ireland a 22-15 defeat at Rome's Olympic Stadium on what was veteran Andrea Lo Cicero's 103rd and final appearance for the Azzurri.
Italy had started this campaign with a 23-18 victory over France and after defeats to Scotland, England and Wales sealed it with another deserved win over another of the pre-tournament favourites.
Italy have now won twice in the Six Nations for only the second time, the last being in 2007.
Ireland, missing fly-half Jonathan Sexton to a foot injury, 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 Brian O'Driscoll, possibly playing his last Ireland international, sent to the sin-bin.
Ireland were robbed several times at their own lineout and it was after Sergio Parisse outjumped Donnacha Ryan deep in Irish territory that the referee whistled for a penalty which Orquera fired over to level on 13 minutes.
Italy resumed in positive fashion, Edoardo Gori dancing through several green shirts before offloading to Parisse at the halfway line where a lineout was called after he failed to release the ball quickly enough.
When Sean O'Brien failed to get up quickly enough after a tackle, Italy were awarded another penalty but Orquera's effort from 40 metres came off the upright.
It failed to faze the hosts, who went 6-3 up thanks to Orquera's penalty after Cian Healy failed to roll away after tackling Parisse.
Ireland suffered further setback when Keith Earls was brought down and forced off after appearing to injure his shoulder.
Luke Marshall was then forced off holding his arm and O'Driscoll was sin-binned for a needless stamp on the chest of Favaro.
Italy ultimately failed to capitalise and it took a penalty from Gonzalo Garcia just before half-time to bring up their lead to 9-3, only for Ireland to reduce the arrears through another Jackson penalty on the stroke of half-time.
Italy had Ireland on the ropes in the opening few minutes of the second half and were finally rewarded with their only try of the game thanks to Giovambattista Venditti, who squeezed the ball over on the right.
Orquera, from 35 metres out, converted to give Italy a 16-6 lead which had the crowd in raptures.
Ireland, however, came fighting back and cut the deficit through a Jackson penalty after Parisse was sent to the sin-bin for a trip on Madigan.
Jackson was spot-on again from over 40 metres moments later after Italy had failed to release, taking the score to 16-12 just before the hour.
With Parisse still sidelined, Ireland began to push deep into Italian territory and came close to making the breakthrough after a dominant 20-phase spell in which they finally had to settle for a penalty.
Jackson converted for 16-15.
Parisse returned, but moments later it was to say farewell to a tearful Lo Cicero who ended his Italy career in the 64th minute and was replaced by Michele Rizzo.
Another chance to extend the lead was spurned when Garcia's penalty effort was short and wide.
But when Orquera was restored to kicking duties minutes later he sent Italy 19-15 in front with another low effort 10 minutes from the final whistle.
After Parisse was brought down by several green shirts as he charged down the left 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.