With Danny Blind gone, new boss Fred Grim was seeking a debut win and a morale-boosting victory to revitalise a struggling Dutch side, but came out second best in his first game in charge.
Italy's Alessio Romagnoli gave the hosts the early lead after he scored an own goal in the 10th minute, only for the visitors to reply almost immediately when Eder converted shortly after before Bonucci sealed the win with a goal just past the half-hour mark with Gian Piero Ventura's side now undefeated in their last seven matches.
The hosts began on the front foot, with their up-tempo attack producing the game's first chance five minutes in when Jermain Lens headed the ball over the cross-bar, but were rewarded shortly after with the lead when Davy Klaassen played a pass through to Quincy Promes whose cross ricocheted off Romagnoli past Gianluigi Donnarumma.
Italy found themselves level back on level terms within seconds after Wesley Hoedt's header fell into the path of Eder as the Inter Milan striker played the ball coolly past Jeroen Zoet.
Bruno Martins Indi came close to giving the Netherlands the lead with his powerful header hitting the crossbar from a Depay corner, but Italy's finishing prowess proved to good as they went ahead after 32 minutes when Bonucci latched onto a loose ball and fired it into the back of the net.
The Dutch came close to levelling with Depay setting up a moove that almost saw Klaassen connect on a Lens cross, only for Daniele Rugani to clear the danger as the Olympique Lyonnais winger pouncing on a misplaced Bonucci back pass, playing through Promes who drew a diving save from Donnarumma.
Ventura introduced Leonardo Spinazzola for his debut with the 24 year-old almost setting up Marco Veratti whose shot was blocked by Tonny Vilhena, whilst Donnarumma made two brilliant saves to deny veteran Dutch midfielder Wesley Sneijder in the closing minutes to help ensure Italy's run of form continued, while Netherlands' woes deepened.
While coming out victors, Italy did suffer a loss with Daniele De Rossi limping off clutching his lower back before the half-time break after taking a challenge as he was replaced by Roberto Gagliardini.