When England thrashed Wales 48-7 in their tournament opener, they were on a 12-match winning run that included beating New Zealand in November.
They have now lost their last three.
If Italy beat Wales in Cardiff next weekend, it would be the first time in a Six Nations that they have won three matches, and they could yet finish third, which would be their best final position.
England dominated possession in the first quarter of an hour but once Italy got the ball in their hands, they immediately looked dangerous and ate up ground.
Garbisi kicked them into a three-point lead on 21 minutes after England gave away a sloppy penalty for offside at their own lineout.
But England had the edge over the feared Italian scrum early on, winning two penalties.
The second one set up England to work an overlap on the left and lock Alex Coles passed to centre Freeman to score the first try of the match.
But Italy were soon back in front after Menoncello ran a superb line to burst between two lumbering England forwards and streak clear for a converted try.
After the Scotland-France try-fest earlier in the day at Murrayfield, this match was one for the purists, but it was tense throughout.
With time ticking down at the end of the first half, Italy turned over the ball and England attacked with verve against a disorganised defence before Finn Smith found Roebuck with a cross-kick to score.
Smith kicked the conversion and the visitors led 12-10 at the break.
Italy were guilty of over-playing the ball at the start of the second half and Smith stretched England’s lead with two penalties, while Nicotera was sent to the sinbin for a cynical infringement.
Just a few minutes later, though, flanker Underhill, who was only in the starting XV because Tom Curry was injured in the warm-up, was given a yellow card for a high shot that survived a bunker review.
Garbisi kicked the penalty and the momentum shifted to the hosts.
The No 10 knocked another penalty in off the post and England’s lead was 18-16 with 20 minutes left.
England’s discipline deserted them and Itoje was next to be sent to the bin as the penalties racked up, with Garbisi kicking to the corner this time as Italy had a two-man advantage for a few minutes.
But England managed to drag Italy’s catch-and-drive into touch to survive.
But before Itoje could rejoin the action, Italy struck with a brilliant break down the left as Menoncello fed Marin to score the history-making try.