Chris Paterson kicked Scotland to victory with two minutes remaining of their RBS 6 Nations Championship clash with Italy at the Stadio Flaminio.
The home side took the lead in the sixth minute when Mirco Bergamasco dived over after collecting Ramiro Pez's chip over the top.
But Scotland levelled when Paterson swooped from close range after replacement Mike Blair was held up just short.
Gordon Ross edged Scotland ahead with a drop but Pez levelled with a penalty before Paterson struck at the death.
Italy sensed another victory in Rome over Scotland and Berbizier sent Carlo Festuccia on instead of Ongaro to further fire the front front-row battle.
Hadden replaced Ross, who had done little wrong, with Parks in a role reversal of what had happened in the four previous Six Nations games this year.
And the Scotland coach also substituted Scott Murray, equalling Gordon Bulloch's mark as his country's most capped forward with 75, with Alastair Kellock.
Italy were looking the more likely to claim the lead and it took splendid scrambling defence from the Scots - notably Hines - to keep an aggressive Bergamasco run at bay.
That move had come from a loose Lamont pass and it was clearly one too many for Hadden's liking as he immediately replaced him with Simon Webster.
A big hit from White caused a turnover for Scotland in the 76th minute and Italy were penalised as they tried to retrieve possession.
Paterson stepped up and from just inside the home side's half kicked Scotland to victory with little over two minutes remaining.
Scotland coach Frank Hadden paid tribute to Italy after his side claimed a hard-fought 13-10 win in their final RBS 6 Nations Championship match in Rome.
Hadden told BBC Sport: "The Italians have made so much progress this year.
"They have played better and we knew it would be extremely tough and a real step up to come to an intimidating place such as this and come away with the win.
"It may not have been pretty but we felt we had the better of the game and were always in control throughout and deserved the outcome."
