Kirsty Smith gave Hibs the lead after only 5 minutes with a curled effort from outside the box.
Celtic levelled instantly, as a defensive error let in Ruesha Littlejohn to score past Jenna Fife.
Megan Cunningham got down well to turn away a Katey Turner shot for Hibs but the holders regained the lead 10 minutes before the break, as Lucy Graham netted after several Celtic attempts to clear the ball failed.
Just a minute in to the second half and it was 3-1, Rachel McLauchlan with a clinical finish from Turner’s cross.
Hibs sealed the cup with a fourth goal a dozen minutes from time, Lia Tweedie driving through the defence to set up Rachel Small to slot home.
