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.
England, who had won their previous nine matches, are bottom of the group, while Italy went top. Norway and Israel occupy the middle two places with one point each.
Israeli captain Nir Biton put the hosts ahead with a 16th-minute penalty after Norway had dominated the opening phase of play.
It was a first goal for Israel in a finals after they lost all three group fixtures in 2007, their only previous appearance, without scoring.
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.
The Norwegians pressed forward despite their numerical disadvantage and hit the post twice and the crossbar once but were punished when Alon Turgeman gave Israel the lead in the 71st minute.
They looked tired towards the end but mounted a late assault on the Israeli goal and were rewarded with a draw when substitute Harmeet Singh scored in the first minute of injury time.
In the first Group B action on Thursday, Spain play Russia and Germany clash with the Netherlands. The two top finishers in each group play in the semi-finals next Saturday with the final in Jerusalem on June 18.
