Ademola Lookman is the sixth player to score a hat-trick in a European final, the first since 1975.
All eyes were on Dublin for Leverkusen’s unbeaten streak, but Atalanta and Lookman were unconcerned about it.
Since his appointment in 2016, Gasperini has transformed Atalanta, which was once a yo-yo club, into European regulars; nevertheless, a trophy is still absent.
Atalanta had lost all three Coppa Italia finals under Gasperini, including last week to Juventus.
They were fired up for the biggest game in their history and came flying out of the traps.
Zappacosta found space and his cutback was fired home by London-born Nigeria international Lookman, a 2022 signing from German side RB Leipzig.
Several figures from Atalanta’s bench ran onto the pitch to celebrate the goal, such was the importance of it.
The ex-Everton, Fulham and Leicester man doubled their lead – and they never really looked back.
It was the quickest two-goal lead a team have had in the tournament final since Liverpool against Alaves in 2001 when it was called the Uefa Cup.
And Lookman had one more great moment in store, as he bamboozled Tapsoba before netting only the sixth European final hat-trick.
The last was all the way back in the 1975 Uefa Cup final by Jupp Heynckes for Borussia Monchengladbach.
Leverkusen finally beaten
This is still a season that will live forever in the history of Bayer Leverkusen, who became the first team to go unbeaten in a Bundesliga season.
No European defeat can take that away from them. But the dream of the first unbeaten season by a team in European competition is over. For the first time in 361 days they tasted defeat.
Even at 2-0 down the stats still said they had hope. They had fallen two goals behind four times already this season and come back every time.
There were little moments, like Alex Grimaldo’s chip being saved and Xhaka missing the target – but not enough of them or with enough quality.
There was a video assistant referee check for a Leverkusen penalty in the final minute, which was not awarded, but the German side barely complained as they knew there was no coming back this time.
Alonso must now pick his team up quickly from one of the first setbacks of his managerial career. On Saturday, they have a German Cup final against second-tier Kaiserslautern in Berlin as they look to complete a domestic double.