Italy, who had lost all 20 previous meetings and who were thrashed at home by Ireland last week, stunned Twickenham with a fourth-minute try by Sergio Parisse but England eventually settled to lead 15-5 at the break after a pushover try by Billy Vunipola and a scintillating effort by Joseph.
Luca Morisi rocked England with an excellent individual try soon after the restart but England regained the initiative with a tap-and-go score by Ben Youngs before good work by Ford opened a hole that Joseph roared through for his second.
Danny Cipriani came on for his first taste of the Six Nations in seven years and scored a try within a minute, Nick Easter charged over for the sixth before Morisi scored his second at the end for Italy.