The Azzurri were on top for large parts of the match and were rewarded with a goal from Simone Zaza three-quarters of the way through, only for Domenico Criscito to be shown a straight red a minute or so later.
As momentum swung the visitors' way in Turin, Nathan Ake popped up unmarked two minutes from time to earn the Oranje a credible draw at the end of what was an entertaining match between the 2018 World Cup absentees.
Italy thought that they were a goal up inside the opening three minutes, with a delayed offside flag cutting short Andrea Belotti's celebrations once flicking home Christophe Bryan Cristante's free kick.
The next clear-cut chance in a first half dominated by the hosts once again fell to Belotti, who this time beat the offside trap but failed to prod the ball through the legs of Jasper Cillessen with just the keeper to beat.
Simone Verdi was unable to pick out Belotti, and Cristante's follow-up was parried by Cillessen as the four-time World Cup winners continued to probe away.
Cillessen was required again later in the half, this time getting a fingertip to Verdi's shot following Jorginho's latest sublime pass over the top of the visitors' five-man defence.
Verdi also hammered the ball over the bar from 12 yards when picked out by Lorenzo Insigne in a good position, and Ruud Vormer was perfectly positioned on the line to nod clear Criscito's glanced header from a corner as the sides went into the interval all square.
The Netherlands looked more assured in possession after the restart and created a little more, with a wicked deflection off Criscito proving awkward for a back-peddling Mattia Perin.
Italy were the side that took the lead, though, with a nice passing move culminating in substitute Federico Chiesa sending a dangerous cross into the middle, which Virgil van Dijk diverted against another sub in Zaza.
The ball ricocheted past Cillessen to give the Azzurri lift off, yet a minute later they were reduced to 10 men after last man Criscito fouled Ryan Babel.
Seeking a first win on Italian soil at the ninth attempt, the Oranje came close to a leveller through Depay's on-target free kick, which Perin did well to push aside.
Vilhena then sent a shot spinning past the target from the edge of the box and Steven Berghuis's curler was pushed wide by an increasingly busy Perin.
The visiting side eventually found a way through thanks to Ake's well-taken header at the end of another right-sided Berghuis cross, making it four successive 1-1 draws in Turin for the Azzurri.
ITALY (4-3-3): Perin; Zappacosta (De Sciglio 59'), Rugani, Romagnoli, Criscito; Cristante, Jorginho (Baselli 78'), Bonaventura (Pellegrini 87'); Verdi (Chiesa 61'), Belotti (Zaza 63'), Insigne (Bonucci 70')
NETHERLANDS (3-5-2): Cillessen; De Ligt, Van Dijk, Blind (Weghorst 78'); Hateboer (Janmaat 46'), Wijnaldum, De Roon (Promes 78'), Vormer (Berghuis 70'), Vilhena; Babel (Elia 82'), Depay