Hibs had struggled to create chances and saw top goalscorer Leigh Griffiths carried off on a stretcher after Hearts midfielder Darren Barr accidentally stood on his ankle.
But their fans did not care in the slightest that their win was far scrappier than Hearts' 5-1 Hampden triumph, or that their 83rd-minute winner came from a fortunate own goal as they celebrated their first derby victory in 13 matches.
Hibs went into the game nine points above Hearts in second place in the SPL but they struggled to get forward in the first half. Finding Arvydas Novikovas early appeared to be a key facet to Hearts boss John McGlynn's tactics and Ryan Stevenson did so with a crossfield ball after two minutes that led to the first chance.
The Lithuanian sent over a deep cross that found Callum Paterson but his header was blocked by the legs of Williams. Jamie McDonald punched clear two inswinging free-kicks by Griffiths and Tom Taiwo shot over from 20 yards but it proved a false dawn for Hibs.
Hearts continued to find Novikovas in space down the left. The Lithuanian fired well wide when a cross would have been a better option before sending over a deep centre that drifted past Ben Williams and bounced off the outside of the post.
Novikovas failed to appear after the break with Andrew Driver taking his place and Hibs created the first chance of the half but Eoin Doyle just could not reach Wotherspoon's flick-on. They suffered a huge blow in the 51st minute when top goalscorer Griffiths was carried off after failing to get up following his tangle with Barr.
Ross Caldwell came on and Barr himself soon limped off with a less serious looking knock with Scott Robinson taking his place. Doyle was close to another Wotherspoon delivery before being replaced by Ivan Sproule, while John Sutton came on for the visitors.
A breakthrough looked unlikely until the 83rd minute. Paul Cairney switched the ball to Wotherspoon on the right wing after a Hearts attack broke down and the midfielder unleashed a shot, which took a heavy deflection off Zaliukas and flew into the far corner.
Hearts threw men forward in a bid to hold on to their trophy but they could only create one half chance which Paterson fired over from 20 yards.
Source: PA
Source: PA