At the Sky Dome, Coventry, who have released Chris Allen after only a couple of months, fell behind on 10.58 to an Owen Fussey goal.
Danny Stewart, got the Blaze back in the match, six minutes into the second period when he scored a powerplay goal, assisted by Derek Campbell and Russ Cowley.
Campbell then turned goalscorer when he fired home on 37.20, assisted by Arron Neil and Danny Stewart.
It looked like Paul Thompson's side would go on to win the match but Edinburgh had other ideas.
Dan Welch equalised on 42.19 and forty seconds from time, Jeff Hutchins shocked the home fans by hitting the winner for Edinburgh.
On Saturday night, Coventry travel to Cardiff before facing Nottingham Panthers at home on Sunday.