Nedim Bajrami stunned the Italians and delighted a huge Albanian support in Dortmund as he smashed in the opener after just 23 seconds, his strike pulverising the previous record for the quickest goal at the Euros of 67 seconds by Dmitri Kirichenko of Russia in 2004.
Yet Italy's response to falling behind was quick too, as Alessandro Bastoni headed the Azzurri level on 11 minutes and Nicolo Barella's glorious effort put them ahead just past the quarter-hour mark.
From then on Luciano Spalletti's team looked much more assured, although they really should have won by a greater margin rather than face an anxious finale as Albania pushed for an equaliser.
Their performance -– the first 23 seconds apart -– was largely encouraging before an enticing showdown with fellow heavyweights Spain in nearby Gelsenkirchen next Thursday.
Whatever happens in that match, Italy are already well-placed to advance to the knockout phase of Euro 2024 from Group B, in which Spain defeated Croatia 3-0 earlier on Saturday in Berlin.
Italy are in some ways an unknown quantity coming into this tournament, with the reigning champions having also missed the last two World Cups and failed to fully convince during qualifying.
Only five of Italy's line-up at kick-off here started the final of the last Euros three years ago, with a new-look team featuring Bologna centre-back Riccardo Calafiori winning just his third cap.
Bajrami makes history
Albania, though, are appearing at just their second major tournament having also gone to Euro 2016.
The novelty of the experience for them helps explain why the home of Borussia Dortmund was a sea of excitable Albanian fans decked in red and black who made up the vast majority of the crowd.
They could hardly believe it when their team, coached by the Brazilian former Arsenal and Barcelona left-back Sylvinho, opened the scoring almost straight from kick-off.
Italy's Federico Dimarco took a throw from the left-back position but played it loosely back into his own box. Bastoni was caught on the back foot, and Bajrami –- who plays in Italy for Sassuolo -- pounced to control and fire past Gianluigi Donnarumma at the goalkeeper's near post.
It was a similar start to Italy's last European Championship match, when Luke Shaw put England ahead inside two minutes in the final at Wembley in 2021 before the Azzurri came back to win on penalties.
This time they drew level when Dimarco and Lorenzo Pellegrini played a short corner routine on the left before the latter crossed for Inter Milan centre-back Bastoni to head in at the back post.
Italy had regained their composure and soon went in front on 16 minutes, a Jasir Asani clearance dropping straight to another Inter player in Barella, who made the cleanest of contacts at the edge of the area to send a first-time shot past goalkeeper Thomas Strakosha.
They should have added to their lead before the interval, with Davide Frattesi hitting the post after meeting a lovely reverse pass by Gianluca Scamacca in the box.
Scamacca was then denied by Strakosha, while Fedrico Chiesa curled a shot just wide on the hour mark.
Italy then sat back, but Albania did not manage another attempt on target and the second-lowest ranked nation in the competition could not find an equaliser despite their best efforts late on.
Substitute Rey Manaj came closest after getting in behind in the 90th minute, but he could not beat Donnarumma.
