Italy had never scored more than 13 points or one try against England but crossed the line four times.
The hosts scored after just 30 seconds but tries from Lauren Cattell, Katie Mason and Lotte Clapp gave England a seven-point lead at half-time.
Italy cut the gap to two points but Abbie Scott and Bianca Blackburn scored to build a decisive advantage.
England, who beat Scotland 32-0 in Cumbernauld last weekend, had no time to settle at Stadio Gino Pistoni as Maria Grazia Cioffi went over following a break from influential full-back Manuela Furlan.
In a pulsating start Cattell brought England back into the match and Mason added a second try following sustained pressure from the forwards.
Sofia Stefan sprinted down the wing to reduce the deficit but Clapp touched down in the corner.
Italy pressed after the interval and the forwards drove over for another score, but a powerful burst from Scott and some fluent play created replacement Blackburn's try, which appeared to have made the game safe for England.
The home side continued to enjoy significant possession and Silvia Folli got a try back under the posts, but England held firm and are next in action at home to Ireland on 27 February.
England women maintained their 100% start to the Six Nations with five tries in a hard-fought win in Ivrea.