Nedim Bajrami created history when he scored for Albania after 23 seconds, with his effort proving to be the fastest goal of all time at a European Championship.
However, Alessandro Bastoni levelled the scores in the 11th minute, before Nicolo Barella sent Italy ahead five minutes later, and the defending champions managed to navigate their way to all three points in their Group B opener.
Spain set the tone in Group B earlier in the evening with a three-goal success over Croatia, and it is shaping up to be a fascinating section, with Albania certainly up against it when it comes to progression to the knockout round of the competition.
Italy overcome early shock to triumph in Group B
There were no major surprises in the Italy side, with Barella featuring in midfield after recovering from a thigh issue, while Gianluca Scamacca was given the nod down the middle.
As for Albania, a 4-2-3-1 formation had Chelsea's Armando Broja at centre-forward, while Atalanta BC's Berat Djimsiti captained the team from the middle of the defence.
Incredibly, Albania made the breakthrough after 23 seconds - the fastest goal in European Championship history - with Bajrami smashing one past Italy goalkeeper Gianluigi Donnarumma after a mistake from Federico Dimarco, with the defender's loose throw finding the Albania attacker inside the Italy box.
There was almost an instant response from Lorenzo Pellegrini, but the attacker fired his effort wide after a clever flick from Scamacca.
Italy did manage to level in the 11th minute, though, with Bastoni's header from a short corner looping into the back of the net, with Thomas Strakosha unable to make the save.
The holders then took the lead in the 16th minute, with Barella's strike from outside the penalty box finding a route past Strakosha, who was unsighted.
Italy join Spain on three points in Group B
Albania had made such a positive start, but Italy were in control from that point forward, and it almost became 3-1 in the 33rd minute, with Davide Frattesi's effort from inside the box coming off the post.
Italy had another opportunity late in the first period, but Scamacca was denied by the Albanian goalkeeper, with Luciano Spalletti's side dominating the contest after their poor start.
Pellegrini had another chance in first-half stoppage time, but he somehow guided the ball wide from close range, with Albania given a huge let-off in the final stages of the opening 45 minutes.
Strakosha made another big save to deny Frattesi early in the second period, and although the offside flag was raised, it would have been a very tight call if the midfielder had found the back of the net.
Federico Chiesa whistled one wide just before the hour, but Albania, in just their second-ever European Championship, did show improvement in the second period and almost levelled late on through Rey Manaj, only for the substitute's effort to be turned behind by Donnarumma's back.
Italy ultimately held on for all three points, with the defending champions joining Spain on three points in Group B, while Sylvinho's side are on zero points with Croatia.
When are Italy, Albania next in action?
Next up for Italy is a clash against Spain on June 20, and La Roja will enter that match off the back of an impressive 3-0 victory over Croatia.
Albania, meanwhile, will tackle Croatia on June 19, with both sides under pressure to triumph due to their losses on the opening matchday.