Hodgson converted his own try and centre Mike Tindall's first-half effort, while he also landed a penalty, but England led only 7-6 at the break.
Wing Mark Cueto's 11th try in 13 Tests took England out of sight just after Lawrence Dallaglio arrived from the replacements' bench with 15 minutes left.
Two more Hodgson conversions meant he finished with 16 points after substitute James Simpson-Daniel claimed a late fourth touchdown.
England's three previous Six Nations trips to Rome had seen them average 51 points a time but Italy are made of sterner stuff these days under French coach Pierre Berbizier and they briefly enjoyed a 9-7 advantage through two drop-goals and a penalty from former Leicester fly-half Ramiro Pez.
Centre Mirco Bergamasco scored a consolation try with a minute left, converted by Pez, and not even the most ardent English fan could complain.
England performed impressively only in patches yet head coach Andy Robinson has now seen his team win six of their last seven Tests, and they will travel confidently to face Scotland at Murrayfield when the Six Nations resumes on February 25.
There were impressive contributions from Hodgson, Worsley and Tindall, who produced his best Test match display since the 2003 World Cup final, but England also find themselves with several areas to work on.
Their ball-retention was occasionally poor and they were repeatedly slow to react in broken play.
Italy, meanwhile, can take great encouragement from their performance - albeit after a fourth successive Six Nations home defeat against England - and they will certainly relish tackling Scotland in Rome next month.