Italy end winless streak in Estonia
Estonia opened the scoring in the 31st minute when forward Sergei Zenjov struck after Italian keeper Salvatore Sirigu lost his grip on the wet ball.
The 2006 world champions patently lacked confidence and did not find an equaliser until the second half when forward Antonio Cassano scored in the 59th minute.
Italy's second came from defender Leonardo Bonucci, who tapped home from close range.
"It's a strong emotion," coach Cesare Prandelli told Rai TV after his first competitive game in charge.
"We had the right reaction and deserved to win. I said at halftime we had to continue doing the right things, but with more speed. We made mistakes on nearly every dead ball we conceded."
Play was interrupted twice in the second half when spectators ran on to the pitch.