Jeremain Lens had put a young Dutch side, whose players averaged 22.3 years, ahead in the 33rd minute and the hosts looked like they were heading for victory as they repeatedly prevented the Italians from netting an equaliser.
Lens picked up a blocked shot from midfielder Kevin Strootman and lifted the ball over Davide Astori before firing home from close range.
In the dying minutes, the Italians stepped up their efforts for a goal and Pablo Osvaldo and Alberto Gilardino came close to scoring before Verratti picked up the ball in the area chipped it over keeper Tim Krul.
"There is still a lot of work to do to let them play the game I want," Italy coach Cesare Prandelli told reporters.
"It is always difficult to get everyone focused for matches like this and only the final 20 minutes we played fierce and aggressive and that paid off."
Prandelli was disappointed with the performance of his strikers Stephan El Shaarawy and Mario Balotteli, who barely troubled the Dutch defence.
Playmaker Andrea Pirlo twice delivered long-range passes to set up Balotelli in the first half but the striker fired wide the first time and had his second attempt blocked by defender Bruno Martins Indi.
"The expectations of Balotelli and El Shaarawy were high [due to] their status at their clubs but now it is time for them to take responsibility in the national team and deliver," Prandelli added.
The stand-out player for the Dutch was 19-year-old playmaker Adam Maher, who connected well with striker Robin van Persie, although the youngster wasted his first two chances which were saved by Gianluigi Buffon.
"Maher played a good match, although he also made some wrong choices," Netherlands coach Louis van Gaal told reporters.
"But I am satisfied with how we played as I demanded that we put them under pressure and that gave the Italians some problems."
