Owen Farrell, George Ford and Jack Nowell added one apiece and Farrell kicked four conversions and a penalty.
The score was harsh on Italy who resisted bravely until a flurry of England tries in the closing minutes.
The winners of the last two wooden spoons were refreshingly positive and replied with two tries of their own from Tommaso Benvenuti and Mattia Bellini with Tommaso Allan kicking a conversion and penalty.
England, who have won all 24 games against Italy, lost halfback Ben Youngs in the first half when he suffered a knee injury.
"They played exceptionally well," England head coach Eddie Jones said.
"It was a tough game of rugby but we ran away with it in the end.
"We let them into the game a bit with individual discipline lapses but, in general, everything was positive."
Watson finished off two flowing moves in the first 10 minutes as England took quick control but Italy reduced the arrears with a superb effort when Allen's looping pass set up Benvenuti for a converted try.
England went in with a 17-10 half-time lead after Farrell scored and converted a try and Allan replied with a penalty for Italy.
Italy's Tommaso Boni had a try chalked off for a forward pass following a video review early in the second half.
Simmonds then raced away to scored England's fourth try although Italy, who lost 10 out of 11 matches last year, continued to cause trouble and again reduced the arrears as Bellini forced his way past Mike Brown to score in the corner.
The referee confirmed the points after the video replay showed Bellini just stayed inside the touchline.
But England floored the hosts with three quick tries in the closing minutes from Ford, Simmonds and Nowell to seal an emphatic victory.