The afternoon started brightly with Drey Wright notching his first goal for the club in the opening minutes as we dominated the early stages.
Yet, after around 20 minutes of the game, Hearts gained control and would run out deserved winners in the end thanks to a double from Andy Halliday - either side of an effort from Stephen Kingsley.
Shaun Maloney made two changes from the side held by Dundee United last weekend. Goalkeeper Matt Macey returned from injury at the expense of Kevin Dąbrowski, who dropped to the bench.
He was joined there by Sylvester Jasper as Wright replaced him in the starting XI. Harry Clarke retained his starting berth after his fantastic debut last weekend.
We remained without the services of Paul McGinn, Kyle Magennis, Demetri Mitchell, Christian Doidge and Kevin Nisbet through injury, along with the suspended Ryan Porteous this afternoon.

Paul Hanlon and Craig Gordon led out their respective sides into a raucous atmosphere and we shaped up in our usual 3-4-2-1 formation.
From the first whistle we were pressing our city rivals high up the park and there were plenty of full-blooded challenges from both sets of players in the opening moments.
Hearts were the first to threaten when Alex Cochrane’s shot from 22 yards was deflected wide of Macey’s near post for the game’s first corner kick.
We opened the scoring in the fourth minute when Wright latched onto Clarke’s ball on the right before stepping away from Cochrane and striking an angled drive that took a slight deflection to beat Gordon.
The home side were rattled, and it could have been worse for them when Craig Halkett slipped in possession on the edge of his box only for Wright to drag a shot wide of goal.
The Hearts defender looked a lot more assured two minutes later when he produced a last-gasp block to deny Elias Melkersen following a threaded ball from Joe Newell.
Despite our impressive start we had a let off on 12 minutes when Liam Boyce got in behind and with only Macey to beat, he took a heavy touch that allowed the goalkeeper to gather.
The home side should have levelled soon after when Barrie McKay’s through ball released Ellis Simms on goal, he dinked it over Macey and wide of goal.
Hearts began to pen us back and they again went close when Nathaniel Atkinson headed off the crossbar from McKay’s delivery.
Halliday then had a couple of opportunities without testing Macey before we suffered a blow when scorer Wright pulled up and had to be replaced by Josh Campbell.
As half-time loomed we nearly extended our lead when Newell found Chris Cadden on the right and his low cross was met by Melkersen at the front post, only for the youngster’s effort to flash over the crossbar with Gordon rooted to the spot.
In first half stoppage time Hearts restored parity as Halliday latched onto a loose ball in our box and slammed it into the net via the far post.

Losing an equaliser on the cusp of half-time was disappointing and those feelings were compounded seconds after the restart as Hearts caught us cold and Kingsley guided in Peter Haring’s cross from close range.
We had a chance to level soon after as Cadden dragged a shot wide from the edge of the box however Hearts were dominating possession and territory.
From a McKay corner kick Simms peeled off his marker and his looping header dropped just wide of the far post.
A third Hearts goal was only delayed a matter of minutes and it came once again from Halliday who produced a fine finish from distance to beat Macey.
With our top-six hopes hanging in the balance Maloney brought on Jasper, James Scott and Ewan Henderson to bolster our attacking options.
Despite this, all we could muster in the closing stages was a shot from distance from Jasper that drifted high over Gordon’s crossbar.
Heart of Midlothian: Gordon, Sibbick, Kingsley, Halkett, Atkinson (Moore 83’), Halliday (McEneff 67’), Cochrane, Haring, McKay (Ginnelly 87’), Boyce, Simms (Mackay-Steven 87’). Substitutes not used: Stewart, Woodburn, Kirk.
Hibernian: Macey, Bushiri, Hanlon, Doig (Jasper 60’), Clarke, Cadden, Doyle-Hayes (Henderson 70’), Newell, Wright (Campbell 37’), Mueller, Melkerson (Scott 60’). Substitutes not used: Dabrowski, Allan, Delferriere, Hauge, Stevenson.
Referee: Nick Walsh.
Attendance: 19,041.