The Italians made their first European final in 33 years and will face West Ham United in the showpiece match in Prague on June 7 after the Londoners beat AZ Alkmaar in their semi-final.
Fiorentina became the first club to reach the finals of four UEFA competitions, having played in European Cup, UEFA Cup, and Cup Winners’ Cup finals. They last reached a European final when they lost to Juventus in the UEFA Cup competition in 1990.
‘Tonight we played like a mature team,’ Fiore manager Vincenzo Italiano told DAZN. ‘It’s my first season in Europe and reaching the final is a great satisfaction. This path to the final will always remain with us but now we have a mission to complete.’
Fiorentina were chasing the game after Basel won the first leg 2-1 but they had trouble finding space as the Swiss employed a deep defensive strategy and sought to counter-attack.
However as the half wore on Basel’s defence began to falter, despite enthusiastic support from the St Jakob-Park crowd, and the visitors looked more likely to score.
Fiorentina took the lead in the 35th minute when a corner was met by the unmarked Nicolas Gonzalez, who headed home to level the aggregate score at 2-2.
Just before the break goalkeeper Marwin Hitz came to Basel’s rescue with a remarkable one-handed save from Giacomo Bonaventura’s effort to prevent another header finding the net.
Zeki Amdouni then scored for Basel 10 minutes into the second half before Gonzalez responded in the 72nd with a well-placed shot, sending the match into extra time.
Hitz made another crucial save in the opening minutes of extra time when he blocked substitute Luka Jovic’s header with another stunning one-handed reflex save.
The match was stopped for eight minutes near the end of extra time so medical assistance could be given in the stands.
Then nine minutes into stoppage time in the extra period Barak collected a loose ball inside the box and slotted it home from close range to send Fiorentina into the final.
After nearly three decades, Italian teams have reached the finals of all three European competitions, with Inter Milan facing Manchester City in the Champions League showpiece and AS Roma meeting Sevilla in the Europa League final.