Italy were held by Poland and the Netherlands played out a stalemate with Bosnia-Herzegovina, leaving Group A1 wide open at the midway stage.
De Boer kicked off his reign with a disappointing 1-0 friendly defeat to Mexico last week, and the display in Zenica four days later was not much better.
The Netherlands did beat Poland 1-0 in their opening Group A1 game in September, however, giving them four points from their opening three matches.
That is one point fewer than Italy, who top the standings despite a stalemate of their own on Sunday.
Federico Chiesa had Italy's best chance of the match in Gdansk, firing wide from close range in a game of few clear-cut opportunities at either end.
The Azzurri's blunt attacking display was in stark contrast to four days prior when putting six unanswered goals past minnows Moldova in a friendly match.
Roberto Mancini's side have now drawn two and won one of their three Group A1 matches, while overall their unbeaten run spans spans 18 matches since September 2018.
Italy have the better overall record in previous meetings with the Netherlands, too, winning nine and losing three of their past 22 encounters.
Indeed, the Dutch are without a victory in six meetings with Italy since a 3-0 win in their opening fixture at Euro 2008.
Italy Nations League form: DWD
Italy form (all competitions): WWDWWD
Netherlands Nations League form: WLD
Netherlands form (all competitions): DWWLLD
Memphis Depay missed the Bosnia draw through suspension but is back in contention here and will likely lead the line in place of De Jong.
Georginio Wijnaldum was the only midfield player to retain his place in the side between the loss to Mexico and draw with Bosnia, but it is unlikely that he will be given a rest.
After being brought on as a second-half sub in Zenica, Steven Berghuis will be pushing for inclusion out wide on Wednesday.
Stephan El Shaarawy is battling with Pellegrini and Chiesa for a starting spot out wide, assuming Mancini sticks with his favoured 4-3-3 setup.
Italy possible starting lineup:
Donnarumma; Florenzi, Bonucci, Chiellini, Biraghi; Verratti, Jorginho, Barella; Chiesa, Immobile, El Shaarawy
Netherlands possible starting lineup:
Cillessen; Dumfries, De Vrij, Van Dijk, Blind; De Roon, De Jong, Wijnaldum; Berghuis, Depay, Promes
We say: Italy 2-1 Netherlands
De Boer told his players to "look at themselves in the mirror" following Sunday's stalemate with Bosnia, which saw his side go a third game without scoring.
Italy also fired a blank last time out but have otherwise netted freely of late and enter this game unbeaten in 18 - a run which we can see them extending with a big win in midweek.