Scotland coach Matt Williams said the pressure had been removed from his side after their first 2005 Six Nations win came against Italy at Murrayfield. "We were all nervous and had a try disallowed after the interval. If we had scored that, the tension would have disappeared," Williams told BBC Sport.
"I said that they would maul and kick us after the break, but we won the territorial battle.
"Give credit to Italy, we had to fight very hard. That's a tribute to them."
Captain Chris Paterson, who kicked six penalties, said the confidence had returned to the Scotland team followng their 18-10 victory.
"I think it was important victory. Physically, I think they are one of the strongest in the tournament," he said.
"Everybody started with a clean slate when Matt took over after the World Cup. Many players in this team had not won a Six Nations game. The pressure is now off."
Man-of-the-match Sean Lamont, who was denied a late try by a forward pass decision, said: "This was a must win game and thankfully we've come up with the goods. I think everyone will be pleased now."