It briefly looked as though England might become the fall-guys, trailing 9-7 early in a second half they later transformed by claiming three converted tries.
England's three previous Rome visits produced an average scoreline of 51-10 in their favour, but calculators were not required on this occasion as Italy pressed all the right buttons to pose serious problems for Tindall and company.
England, though, remain on course for the RBS 6 Nations Championship title - and a possible first Grand Slam since 2003 - after ending their two-year run of away defeats.
England had lost six games in a row on the road and, while it was not pretty and England hooker Steve Thompson's pre-match prediction of "an 80-minute battle" proved accurate, the visitors took their chances when they eventually gained control.
It was a long time in coming and England could not even begin to think about relaxing until fly-half general Charlie Hodgson sprinted over for a try that he also converted.
That 55th-minute effort left Italy reeling and England sealed the deal with further converted touchdowns from wing Mark Cueto - his 11th in 13 Tests - and substitute James Simpson-Daniel.
Tindall set the ball rolling with England's opening try on 25 minutes but Italy absorbed everything their opponents could throw at them and trailed only 7-6 at the break.
"Italy, with all the players they've got in the French Championship and the Heineken Cup are a good quality outfit," said Gloucester centre Tindall.
"I don't think you will see anyone smash them and I think you are going to see a big scalp for them before too much longer."
England head coach Andy Robinson hailed Tindall's attacking display as his best in an England shirt and there were further encouraging signs of his midfield partnership with Jamie Noon taking definite shape.
"I said it would take a little time to settle in and it is really," added Tindall. "I didn't get Jamie into the game as much as I wanted to but with Italy's defence it is very hard to do that.
"Jamie and myself are trying to get better. We are still a long way off but it is improving and it is always nice to get a try.
"It is the best feeling in the world when you call a move and it works like that and there was a big hole to go through and score.
"This team is growing and in the second half, we started off-loading a lot more and when you're able to do that it just makes the game a lot easier."
Italy's highly-rated forwards gave as good as they got against the revered England pack and in the end, it was the world champions' extra bit of class behind the scrum that under-pinned a sixth win from seven starts during Martin Corry's leadership reign.
Italian fly-half Ramiro Pez dropped two goals and kicked a penalty while centre Mirco Bergamasco claimed a late consolation try that Pez improved but Pez's opposite number Hodgson had another impressive outing and contributed 16 points to England's cause.