Italy started strongly and led 22-17 after the first quarter although after just over three minutes into the second, a score by Lior Eliyahu tied the game up at 27-27.
With three minutes to go until the half-time break, Italy then pulled clear once again, this time finishing with a 10-2 tear to finish the period - a Bargnani dunk very much the highlight.
Trailing 48-39 heading into the second half, the home team knew they would have to come from behind the same way they did in their previous game against Montenegro but this time it wasn't to be.
They were still behind by nine points going into the fourth quarter and while Eliyahu made it a one shot game at 79-76 with less than ninety seconds remaining, Italy made their free-throws in crunch time to celebrate an impressive win.
As well as Bargnani, Marco Belinelli was instrumental in the success and posted 14 points, eight rebounds and six assists.
Eliyahu finished with 19 points for Israel while Omri Casspi continued his good form with 20 points and 10 rebounds.
"This is a bad moment in our campaign. In fact, after this loss we are starting all over again. Let's face it, they dominated throughout the whole game. We should not lose a home game, we'll have to balance it with a win on the road."
Israel player Yotam Halperin:
"Of course we're all disappointed. We hurt in the first half, especially in defense. It's a moment where we start from the beginning, and we have to come back with a win from Latvia anyway. Bargnani was excellent and we couldn't stop him. I think we made small errors, and because of them we lost but we need to move on."