Floriana got off to a perfect start when Varela slotted home from a free kick after just two minutes.
It got even worse for Hibernians when Fontenalla made it 2-0, with only eight minutes on the clock.
Hibernians regrouped and began to gain control of the game but sideways football put little pressure on Floriana’s defense.
Captain Clayton Failla struck a superb free kick from outside the box to pull one back just before the break.
Hibernians spent most of the second half in the Floriana half and several good chances went begging until Jackson Lima latched onto a cross from the right to level the score with ten minutes remaining.
Drama right at the end as Andre Agius headed an extra time winner for Hibernians to put them four points clear at top of BOV Premiership.