Sergei Zenjov had given Estonia a shock first half lead but second half strikes from Antonio Cassano and Leonardo Bonucci, thanks to some non-existent marking at corners, allowed Prandelli to begin his competitive reign at the Italy helm with a win.
It was the Azzurri's first win of 2010 and their first success in eight matches.
Although Italy had a couple of early half chances, it was Estonia who really threatened first. Zenjov won a challenge in the air with Bonucci and Giorgio Chiellini caught the wrong side of Konstantin Vassiljev, who was breaking from midfield, but the NK Nafta Lendava man volleyed high and wide on 13 minutes.
Italy's response was immediate with Daniele De Rossi releasing Giampaolo Pazzini with a precise throughball, but the Sampdoria forward shot straight at Sergei Pareiko.
Italy were labouring and creating little in terms of clear chances, and their lacklustre approach cost them on 31 minutes. Vassiljev fired in a low free-kick from 35 yards but it was straight at Salvatore Sirigu, who spilled it and Zenjov reacted quickest to slam home the rebound.
That sparked Italy into action, with Pazzini cutting inside from the left, only to fire straight at Pareiko, before Cassano saw his shot finish just wide.
Any hopes Italy fans may have had that their team would come out firing in the second period were almost quashed three minutes after the restart when Sander Puri burst onto a loose ball, bit his shot flashed inches over Sirigu's bar.
However, the game turned on its head in three minutes around the hour mark as Estonia failed to deal with two Andrea Pirlo corners.
Cassano was left unmarked to head home the first from 10 yards and from the second the Sampdoria forward went to the near post and flicked the ball between his legs into the box where Bonucci was left free to control and shoot home from six yards.