"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.
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 past year.
ANTHONY WATSON and Sam Simmonds were England's gladiators as they bagged braces in Rome.
Simmonds then raced away to scored England's fourth try although Italy, who lost 10 out of 11 matches previous year, continued to cause trouble and again reduced the arrears as Bellini forced his way past Mike Brown to score in the corner.
That argues a degree of consistency but, with the 2019 World Cup in Japan slowly coming into focus, it is time for England to step up even further and show just how good they can be. But Simmonds again demonstrated that, while he is not the biggest, his elusive, low-slung style is well suited to the global stage. "If he was a cricketer he would be playing 20-20".
Simmonds, it must be said, gives up almost five stone to Vunipola.
"He's a bit of a freak Simmo, isn't he?" It was not surprising either that his two scores came late on, when his fleetness of foot can exploit fatigue to an even greater extent.
The only negative note for England was an injury to Ben Youngs.
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Victory meant England have won all 24 of their Tests against Italy, with the Azzurri's losing streak in the Six Nations extended to 13 matches. It is relevant because the biggest criticism of Te'o is that for all his hard, straight running, he does not pass the ball often enough.
"Great to get @EnglandRugby #6Nations off to a winning start".
In the 30th minute, Owen Farrell earned his 750th metre in an England shirt. The first was a no-frills, hard carry over the gainline in the Italian 22.
But Watson soon had his second try.
For all that Simmonds and Te'o impressed this was not the "brutal and uncompromising" performance Jones had demanded, not until the final 15 minutes anyway.
Youngs was carted off on a stretcher less than 10 minutes into his 56th start for England, which overtook Matt Dawson's record of most starts for an England scrum-half.
England inched 10 points clear with a penalty from Farrell before Italy had a try ruled out after consultation with the TMO as Allan's pass to send Boni through was forward.
Moody, speaking on behalf of Land Rover, added: 'I can't see Italy causing any upset anywhere during the competition which is a shame because Conor O'Shea and Mike Catt are incredible coaches, ' he added.