In the first derby of the new century, Lawrence Shankland scored two goals for Hearts.
The opener was scored in the first 10 minutes by Will Fish, who made a terrible mistake.
Stephen Humphrys put the game out of reach when he put the game out of reach at the start of the second half.
The three teams are separated by five points in third and eighth places.
With eight defeats in their previous 10 matches, Lee Johnson would have been desperate for his side to start well, but within eight minutes they had hit the self-destruct button.
On his first start for Hibs, Fish wanted too long on the ball to clear his lines and was hunted down and robbed. Josh Ginelly's shot was parried by David Marshall and he was able to score.
The nerves in the Hibs ranks were obvious, failing to keep hold of the ball for any sustained period as Hearts knocked it about confidently.
Kevin Nisbet's shot from 10 yards out was the first chance of goal for the visitors.
After a Robert Snodgrass cross caused chaos in the Hibs box, Toby Sibbick fired home to make the score 2-0. The visitors thought they had dodged a bullet when the goal was ruled out for being out of place.
Kevin Clancy awarded a penalty after a six minute VAR stop. He scored from the spot for his 15th goal of the season.
Fish had a chance to make up for his earlier mistake when he rose to head a free-kick goalwards, but he missed the target.
There was a huge opportunity for Hibs. Sibbick allowed a free run on goal and allowed the Frenchman to take an age setting himself and allow him to make a great recovery tackle.
Johnson tried to turn the tide with two changes at the break, but Fish and Harry were replaced by Kyle Magennis and Aiden McGeady.
The Hibs were indebted to Paul Hanlon for the tackle he made on Devlin.
Chris Cadden shot a shot down Clark's throat. Nisbet's shot on the spin appeared to be destined for the net, but Alex Cochrane blocked it.
The Hibs were having more joy and Youan and McGeady were starting to find gaps in the Hearts defence, but they needed a goal to set the alarm bells ringing.
McKay's strike flew off target after Bushiri made a mistake.
After coming in from his flank, Cadden tried to hit the post with his curling effort, but it flew past the post and Clark beat him.
Cadden put it on a plate for Magennis but he was denied by a double save.
Stephen Humphrys came off the bench to slot home the third goal and send the Hearts fans home happy.
A reliable goal scorer can make all the difference and they don't come much more reliable than Lawrence Shankland.
That was what made the decision.
The most frustrating thing for Lee Johnson will be that Hibs didn't start to show much until they were 2-0 down.
His team looked frightened by the fashion in which they gifted Hearts the lead, with Fish's error seeming to spread nervousness through the rest of the side.
The Hibs dominated the ball after the break and created a lot of chances. They might have taken something from the game if they'd performed like that from the beginning.
Six points from the last 33 is a situation that needs to be gripped sooner than later.
Hibs are away to Motherwell on the same day as the Hearts game.
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