Elliot Daly and Alex Mitchell scored England's two tries with George Ford kicking the rest of the points for Steve Borthwick's men, who claimed their first round one win since 2019.
England are a point behind Ireland, who soundly beat France on Friday, in the Six Nations standings after failing to earn a bonus point in a bitty display in the Italian capital.
The away side were trailing Italy by nine points mid-way through the first half after superb tries by Alessandro Garbisi and Tommaso Allan.
But Gonzalo Quesada's Italy couldn't pull off their first ever win over England on the head coach's debut in the Azzurri dugout.
It was a promising display from the Italians who scored a late converted try through Monty Ioane to earn a defensive bonus point and could have won had Tommaso Allan not missed a key penalty.
Nevertheless, Italy have won just one Six Nations match of their last 43 and have not enjoyed victory at home since 2013.
England, meanwhile, got their bid to win their first Six Nations title in four years up and running ahead of facing Wales at Twickenham next weekend.
