Ruud van Nistelrooy put the Dutch ahead in controversial circumstances after 26 minutes when he scored from close range - but looked suspiciously offside.
Wesley Sneijder swept in a second from Dirk Kuyt's header five minutes later.
Edwin van der Sar then denied Italy with stunning saves from Fabio Grosso and Andrea Pirlo before Giovanni van Bronckhorst headed in after 80 minutes.
Euro 2008 has made a low-key start, but this was a game to set any tournament alight as the Dutch played in a stunning counter-attacking style and Italy also showed flashes of brilliance, despite ending up well beaten.
Holland are in pole position to qualify after France's dismal goalless draw with Romania, but World Cup holders Italy - even in defeat - suggested they can still go through from this tough group.