England dominated the opening stages, and were ahead through Watson's third-minute try. Prop Dan Cole was influential in winning a scrum for the visitors, and from the resulting lineout, Jones's team shifted the ball wide for Watson to squeeze over in the corner.
The game was then stopped for a period after England scrum-half Ben Youngs was forced off with a leg injury - he was helped off on a stretcher and replaced by Danny Care. The injury did not stop England, however, who went over again through Watson on the wing.
Italy finally settled into the game after conceding two tries, and had their best spell of the first half from a penalty won by number eight Sergio Parisse. The hosts made good ground through centre Tommaso Boni, before winger Tommaso Benvenuti crossed to reduce the arrears.
The momentum swung once more after Italy's try, as Owen Farrell coasted through the hosts' defence, which was all at sea, to restore England's advantage. Italy fly-half Tommaso Allan converted a penalty kick in the last action of the first half.
England started brightly in the second half, but Watson was unable to touch down for his hat-trick after a brilliant tackle from flanker Sebastian Negri. Farrell converted a penalty for England, before debutant Simmonds scored to extend the lead on 58 minutes.
Italy would not lie down, however, and went over again through winger Mattia Bellini on the far side - the try had to be sent to the TMO before being confirmed.
England wrapped up the victory with a late George Ford try, before Simmonds produced a no-look pass for replacement Nowell to put gloss on the scoreline.
The result takes England to the top of the Six Nations table ahead of their next game against Wales on Saturday.