Hearts made one change to the side that started the 2-0 win at Dundee United a fortnight ago, with the fit-again Stephen Kingsley starting in defence and Andy Halliday dropping to the bench. New signing Barrie McKay was also among the substitutes.
There were three changes for Hibs as Jake Doyle-Hayes missed out through illness and Jamie Murphy was absent due to injury, while Darren McGregor dropped to the bench.
Joe Newell, Paul Hanlon and Chris Cadden all went straight into the starting line-up after their recent injury lay-offs.
Hearts had the first attempt on goal in the 15th minute when Ben Woodburn rasped a 20-yard strike just over the crossbar.
The visitors struggled to get a proper sight of goal in the early stages although there was a momentary scare for the hosts in the 19th minute when Newell's cross from the left dropped on to the top of the crossbar.
At the other end, Liam Boyce headed over from a Kingsley cross.
Hearts were starting to crank up the pressure and in the 25th minute Gary Mackay-Steven saw a ferocious strike from 25 yards out beaten away by Macey. Kingsley and John Souttar then both went close from successive Hearts corners.
Home goalkeeper Gordon made his first save of the match 10 minutes before the break when he got a firm wrist behind a powerful Martin Boyle strike from outside the box.
The Australia international forced the Scotland stopper into another vital block with a low-angled shot from the edge of the box at the end of the first half.
With Hearts having generally been the more authoritative side before the break, Hibs manager Jack Ross sent on midfield enforcer Alex Gogic in place of James Scott for the start of the second half in an attempt to get his side back in the game.
The visitors had a good chance just before the hour when Kyle Magennis seized on a loose pass from Souttar but the midfielder's shot from 15 yards out was too tame to trouble Gordon.
Mackay-Steven then went close twice in quick succession for Hearts, with the winger denied by big saves from Macey on both occasions.
The Hibs goalkeeper made another important block in the 73rd minute to keep out Josh Ginnelly's header after he was picked out at the back post by a cross from fellow substitute McKay.
At the other end, Gogic fizzed a powerful strike inches wide before Magennis was denied by stunning save from Gordon after being teed up by Kevin Nisbet after 77 minutes. Nisbet then volleyed the ball just over from inside the box.
Hearts almost won it at the death but the excellent Macey prevented Hanlon turning Alex Cochrane's cross into his own net.