Olympiakos flew out of the blocks as they attempted to reward their ferocious support, who had travelled the short distance from Piraeus to the home of their rivals AEK in northern Athens.
It was only the second time a Greek team had reached a European final while Fiorentina were playing in their sixth.
Both sides traded blows in a first half that promised goalmouth action but resulted in few clear chances.
On-loan Wolves midfielder Daniel Podence forced Fiorentina goalkeeper Pietro Terracciano into a fine save down his left in the opening three minutes.
Giacomo Bonaventura should have given Fiorentina the lead but his tentative effort in the box safely dropped into Konstantinos Tzolakis’ arms.
The Italians put together the best move of the night in the second half as right-back Dodo surged forward and found Christian Kouame in space inside the box but his poor contact on the ball allowed Tzolakis to claw it clear.
Extra time was needed and it was El Kaabi – who scored five goals in the semi-finals against Aston Villa – who rose to the occasion again.