Hearts triumphed in the first Edinburgh derby of the season to leave Hibernian bottom of the Scottish Premier League going into the international break.
A tidy finish by Ryan Stevenson gave the hosts the lead on 39 minutes.
Hibs goalkeeper Graham Stack made an incredible save to deny Andy Driver after the break.
But Hearts did get a second when Andy Webster's header crossed the line, despite Akpo Sodje's desperate attempt to clear on the line.
The game was subject to a short delay as stewards had to put out a couple of flairs which had been thrown on to the pitch.
But once underway, the action was typically frantic as both sides tried to get a grip of the game and Hibs' Ivan Sproule picked up an early booking for a crunching challenge on Danny Grainger.
Stevenson survived a penalty appeal when the ball appeared to hit his arm in a crowded Hearts box.
Garry O'Connor nodded wide from Sproule's clever chipped cross as the game began to open up.
Driver forced his way into the Hibs box moments later and retrieved the ball from Sproule's tame clearance but the winger's right-foot shoot was comfortably claimed by Stack.
But Hearts kept up the pressure and took the lead when Jamie Hamill centred for Stevenson to calmly despatch the ball into the net.
Hibs tried to respond and Matt Thornhill ran on to O'Connor's pass, evaded a defender and curled a shot just wide of Marian Kello's left-hand post.
Stephen Elliott drew a block from Stack just after the break and the Hibs keeper then produced an unlikely goal-line intervention to keep the Leith side in the match.
Elliott's initial shot came back off the post and Driver's rebound effort looked certain to find the net until Stack leapt across his line to scoop the ball over the line with his foot.
O'Connor's free kick was gathered at the second attempt by Kello but Hearts continued to dominate and Hamill fired straight at Stack from deep inside the area when a pass to a team-mate would have been a better option.
Hibs sent on new signing Leigh Griffiths and fellow forward Akpo Sodje for Sproule and Junior Agogo to try and turn the match around and Griffiths almost immediately picked up a yellow card for a sliding challenge on Hamill.
Hearts' second came from a corner, which was conceded when Driver's low cross was ushered out by Stack, who should have claimed the ball.
Hamill's superb delivery was bulleted towards goal by the head of Webster, Sodje cleared from behind the goal-line and David Obua's replacement Eggert Jonsson side-footed the ball high into the net.
Both Jonsson and Webster celebrated but television replays showed that it was undoubtedly Webster's goal.
Obua had been taken off after coming off worse in a collision with Stack and another coming together between Kello and Sodje eventually saw the Hearts keeper replaced by Jamie MacDonald.
MacDonald's first contribution was to smother a Griffiths shot after the on-loan Wolves man had cut in from the right and further efforts from O'Connor and Murray failed to make a dent in Hibs' deficit.