Having led 6-0 through two Owen Farrell penalties approaching the break, England conceded a brace of tries before on 37 and 40 minutes to trail 12-6 at the interval.
And given the inexperience of England's new-look side, it would have been easy to lose composure and start to panic but that never happened.
Instead, England held their nerve and struck back with a second Charlie Hodgson charge-down try in as many weeks and a further eight points from the boot of the nerveless Farrell as they avoided a first defeat to the Azzuri.
"The most pleasing thing was that there was no sense of panic," said Lancaster.
"We put ourselves in a good position in the first 20 minutes. I thought we started well then there was a bit of a mad five minutes and we came in down at the half.
"We felt there were one or two areas that we needed to work on, in particular getting balls in the No10's hands early and getting more tempo into the game. I'm pleased we managed to do that.
"Italy missed a couple of kicks and we felt that Owen was fantastic in terms of temperament and the ability to step up and get those kicks to keep our scoreboard ticking over.
"It's a great win for us. It was tough as Italy played extremely well and put us under huge pressure. They made lots of passes and it was very difficult conditions for the players but overall I'm pleased to get the win and we look forward to go to Twickenham in two weeks time."
Next up for England is a home tie with fellow table toppers Wales on February 25.
Both sides have begun their 6 Nations campaigns with two wins from two, with huge battle expected in a fortnight's time.
England have welcomed back star duo Manu Tuilagi and Courtney Lawes into their extended squad ahead of Round 3, while Toby Flood is also under consideration for a place in the matchday 22 having recovered from his knee injury.
And with the likes of replcements Lee Dickson and Ben Morgan impressing in their half-hour cameo's in Rome, Lancaster has plenty of options as he prepares to pick a team capable of beating the in-form Welsh.
"I'm delighted with the impact our substitutes made," added Lancaster.
"Both Dickson and Morgan made a fantastic impact and gave us our best period of the game.
"We've got some players who put their hands up and that's part of what we'll be considering as well as how they contribute and how they train.
"Manu Tuilagi and Courtney Lawes played this weekend (for their clubs) as well. They're good internationals and are playing for a place."