Italy, who qualified for Brazil 2014 with two games to spare, remain unbeaten on 21 points from nine games while Bulgaria, in second, and Denmark are both eight points adrift.
Barzagli was called into the squad following injury to Luca Antonelli, who limped out of a 4-0 friendly win against San Marino in Bologna on Friday.
Brazilian striker Reginaldo came off the bench on the hour mark and 10 minutes later ran on to a through ball to beat compatriot Noberto Neto in the Fiorentina goal with a well-struck shot.
The appointment of manager Brendan Rodgers is one of the biggest gambles in Liverpool's history.
Liverpool manager Brendan Rodgers revealed on Thursday that he hopes to seal two more signings in the next 48 hours.
Liverpool manager Brendan Rodgers has forged a reputation for playing attractive football but the Northern Irishman admits that success must come first as he takes on his new role at Anfield.
Italy midfielder Alberto Aquilani has been transferred from Liverpool to AC Milan.
Former world champions Italy stunned the team who succeeded them just over a year ago with a 2-1 victory over Spain here on Wednesday.