A Farrell penalty gave England a 10-point advantage, which remained intact when Tommaso Boni had a try ruled out for a forward pass, and number eight Simmonds showed a sharp turn of foot to score his first England try after spotting a gap from the back of a ruck.
And if England lack a bit in hard, direct running with Simmonds at No 8 Ben Te'o did his best to make up for it.
The result takes England to the top of the Six Nations table ahead of their next game against Wales on Saturday.
Italy head coach Conor O'Shea is optimistic about his side, claiming they're making good progress.
"Maybe on Sunday after the match it will be a hard evening, but we prepare to win matches and the wonderful thing about sport is that anything can happen", said O'Shea.
"He's got a big match demeanour, he doesn't get too excited or too disappointed and gets on with the next play".
Despite being ineligible for the game in Rome, as he serves a ban for a unsafe tackle on Jamie Roberts, the 75-cap flanker trained with Jones' squad at their Surrey base this week. "It was a good tough game of rugby and we ran away with it in the end".
"Tonight we're going to enjoy it, I want the boys to enjoy the win".
"Obviously [we] got the result we wanted but going to Italy it's a different squad, it's new players, everyone wants to beat England and everybody comes and raises their game for England".
"I don't think we've scrummed as well as that in the time I've been in charge of England", Jones said after his pack laid the platform for a victory of seven tries including two each for the Bath wing Ant Watson and Exeter No.8 Sam Simmonds. They have lost all 23 times they have played England but have come close several times.
The Azzurri are enduring a 12-match losing streak in Rome since beating Ireland in March 2013. For the rest of the Six Nations Jones will surely build his back row around Simmonds, even if that means biting the bullet and dropping one of his three outstanding locks. Ireland have only beaten Les Bleus in the Six Nations twice in Paris (in 2000 and 2014) and lost two of their three away games in the tournament previous year.
England have only lost three of 18 opening day fixtures in the Six Nations, against France in 2014 and Wales in 2005 and 2008.