A goal in injury time for 10-man Norway dampened the festive atmosphere for the hosts, who were forced to settle for a 2-2 draw in the other Group A game.
Israel began staging its most important international sporting event in 45 years amid tight security following a politically-charged build-up.
European football's governing body UEFA had held firm against calls from pro-Palestinian activists to move the tournament away from Israel, who are the weakest of the eight teams competing, because of restrictions on the movement of its athletes.
Italy displayed plenty of skill against England's powerful line-up and came away with the win thanks to Napoli's Lorenzo Insigne, who scored with a curling free-kick in the 79th minute to leave goalkeeper Jack Butland stranded.
Norway levelled in the 24th minute after a defensive error when Marcus Pedersen rattled home a low drive in the area - but the visitors were reduced to 10 men a minute before the break when Vegar Hedenstad was sent off for bringing down Israel's last man, Mohammed Kalibat, as he headed towards goal.
