It moved England top of the table after the first round of matches, with them and Wales both recording wide victories.
The Italian squad had posed for a squad photo at the Colosseum in the run up to the tournament to promote their hopes of avoiding the wooden spoon for a third successive year.
"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.
"Life's full of contradictions and Sam is one of them", Jones said.
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Mattia Bellini scored a second Italy try, but Conor O'Shea's men were unable to avoid a 13th consecutive Six Nations defeat, George Ford, Simmonds and Jack Nowell adding late tries as Italy exhausted. But the scoreline perhaps didn't reflect what we saw on the pitch. Failed to hold first high ball, was turned over when held up in possession and conceded a couple of penalties.
Owen Farrell's long punt from the ensuing penalty brought possession inside the Italian 22 where Maro Itoje claimed the line-out and the English backs worked space for Watson on the opposing flank.
Simmonds might reduce the average weight of the England pack quite considerably - he weighs around two stone less than Billy Vunipola, the man he was replacing at the base of the scrum - but what he lacks in heft he more than makes up for with speed and graft.
Simmonds then raced away to scored England's fourth try although Italy, who lost 10 out of 11 matches a year ago, continued to cause trouble and again reduced the arrears as Bellini forced his way past Mike Brown to score in the corner.
Italy wilted in the closing stages after putting so much effort in and fit-again replacement Nowell helped himself to a seventh try three minutes from time, Farrell failing to convert but England finishing the contest in style with a clash against Wales to come next Saturday. "The tournament (is) only going to get better".
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Allan added the extras and the gap was down to just three points.
Italy appeared to have made a flying start to the second half when Tomasso Boni went over the line, but it was ruled out for a forward pass.
Italy refused to let England get away, however, and Bellini touched down in the left corner in the 58th minute following another wonderful pass from Allan.
England hit back five minutes later when Farrell played a one-two with No10 Ford and converted his own score to spark the Stadio Olimpico's first rendition of the afternoon of Swing Low, Sweet Chariot.
Eventually, tiredness began to show in the home ranks and George Ford finished off another Farrell break before Simmonds stole in for his second.