Ecstatic Olympiakos players hail team spirit after European title win
In a game that was high on intensity and physicality but low on quality in front of goal, neither side could score in the 90 minutes before Ayoub El Kaabi got the winner in the 116th.
"I have no words," said Olympiakos winger Giorgos Masouras as other teammates nearby cried and celebrated with their fans.
"It has not yet sunk in. We did it together. I was certain we would win it and we held on and got it in the end."
"We are now part of Europe's elite and have more responsibilities. We have to maintain this level now."
Olympiakos, who finished third in the league title race, became the first Greek club to lift a European trophy, with Panathinaikos coming closest previously in 1971, when they lost the European Cup final to Ajax.
Celebrations broke out across Athens and the port of Piraeus with thousands of supporters lighting flares and fireworks
"I am very happy and satisfied and it is an honour to have made the fans happy," said Olympiakos coach Jose Luis Mendilibar, who took over in February.
"I am very happy that we achieved something that the club had not achieved before. We will celebrate, we will cheer and then we will get back to work for what comes next."
The result was a second consecutive defeat in the Europa Conference League final for Fiorentina, who had got to the showdown with Olympiakos without losing a single game.