The Gattuso era almost had its first goal within three minutes, when a neat move resulted in a Matteo Politano strike from 20 yards taking the slightest deflection on its way just wide. Italy worked the resulting corner back to Federico Dimarco, whose fierce effort from further out flew past the post.
The Azzurri were unrelenting in their early pressure, but Dimarco missed the target again before Mateo Retegui turned well inside the box and saw his shot go a whisker wide.
For all Italy’s dominance, they did not force Estonia goalkeeper Karl Hein into action until the 20-minute mark, when he batted a Mattia Zaccagni effort straight to Dimarco, but got up quickly to deny the full-back as well.
Politano and Moise Kean were both wasteful from excellent positions, then in stoppage time before the break, Hein was at the double again, making a smart stop to deny Dimarco before reacting superbly to tip a Retegui header over the bar.
It’s the sixth time in seven matches Jurgen Henn’s side have gone in at half-time level, but the second half began with them under just as much pressure as the first. Hein’s defence had already made a few key blocks before his magnificent reflexes denied a Sandro Tonali volley.
He then clutched a Kean header, but Estonia’s resistance was finally broken on 58 minutes when Dimarco’s deflected cross was flicked up by Retegui for Kean to power home with his head.
Kean came close to doubling the lead when he won possession within seconds of the restart and struck the post with Hein beaten.
The floodgates eventually opened when Gattuso brought Giacomo Raspadori on as the match entered its final quarter, as Italy scored twice in three minutes.
First, Raspadori found Retegui, who opened up his body and side-footed a 20-yard effort right into the bottom corner, before Politano got to the byline and clipped a cross for Raspadori to meet with a stooping header and beat Hein.
The goals kept flowing in the closing stages, as Andrea Cambiaso used his pace on the left and crossed for Retegui to head in his second and Italy’s fourth.
Alessandro Bastoni added number five by powering in another header after a quick corner as Italy moved onto six points from three Group I matches, still trailing Norway and Israel having played fewer games.
A 10th successive loss to teams ranked in the world’s top 30 keeps Estonia on three points from five matches.
Flashscore Man of the Match: Giacomo Raspadori (Italy)
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