Going into the tournament's final round next Saturday, England are now second, a point behind France.
It still looks a long shot for England, who face Wales in Cardiff, while France have a home fixture in Paris against Scotland and will be guaranteed the title with a bonus-point victory.
England can keep dreaming, though, after securing a third straight win in this year's Six Nations on Sunday — and this time by a landslide after one-point nailbiters against France and Scotland.
But the bad news for England is that Ollie Lawrence will miss the Wales match and could struggle to play again this season after suffering an Achilles injury.
The Bath centre is set to undergo scans and see a specialist during the next 48 hours after going down hurt in open play after just eight minutes.
"Fingers crossed it is not quite as severe as we fear it might be," coach Steve Borthwick said.
With the score at 14-14 just after the half-hour mark, a 32nd straight victory over the Italians wasn't guaranteed -- but England were ruthless in the second half.
Left winger Ollie Sleightholme finished with two tries — one in each half — while Tom Willis, Tommy Freeman, replacement Marcus Smith, Tom Curry and Ben Earl also went over. Fly-half Fin Smith nailed six of his conversions.
England's only loss so far has been the 27-22 defeat at Ireland in the opening round, so the outlook is positive for coach Steve Borthwick and his players after consecutive losses to New Zealand, Australia and South Africa in the autumn had put the team under pressure.
All England can do now is beat Wales — rivals on a record 16-game losing run — and hope for a favour from Scotland.
Italy had three tries, the best coming from Ross Vintcent when the No. 8 galloped clear after running onto an inside pass from livewire fullback Ange Capuozzo. That converted score brought the teams level at 14-14 after 32 minutes.
Capuozzo and Tommaso Menoncello grabbed the other tries for the Azzurri, who couldn't manage a fourth try for a losing bonus point.
They stayed in fifth place on four points, one more than Wales in the battle to avoid the wooden spoon.
Italy close with a home match against third-place Ireland, who are two points behind France and one behind England.
Italy against Ireland kicks off "Super Saturday" before Wales take on England and then France, minus injured star player Antoine Dupont, tackle Scotland.
