Hodgson was again the only try scorer for the Red Rose as he put pressure on Italy full-back Andrea Masi and blocked his clearing kick, while Owen Farrell was faultless with the boot contributing 12 points.
And while Italy outscored their visitors with first-half tries from Giovanbattista Venditti and Tommaso Benvenuti, Hodgson was delighted with the way England held on after the break.
He said: "We knew we had to keep our composure. We felt we dominated in the first half but they got a lucky try.
"We kept plugging away, we kept our tempo in the second-half, we didn't lose our heads and it came good in the end.
"To show the resolve we have done from 15-6 down, to come back and be successful in a place like this against Italy, with all the experience they had, we've shown what we have and we're delighted to get the win."
Saracens youngster Farrell again impressed from the kicking tee in difficult conditions, while Italy replacement Tobias Botes missed two late shots at goal, and the inside centre revealed that interim head coach Stuart Lancaster had told the team not to panic after conceding two quick tries.
Farrell said: "It was OK at the start, it was pretty still and a bit of snow had settled on the pitch. The wind picked up in the second-half and it started snowing again, it was a bit worse then but not too bad.
"At half-time Stuart Lancaster said to keep doing what we were doing, we don't have to chase. Their tries came more through our mistakes.
"I felt we were still on top in the first-half, credit to the boys, we dug in and got the win."