Hearts now have four wins from 11 matches since their first-team squad first suffered delayed payment of wages, but Hibs have now failed to taste victory in nine matches, have not won the capital clash in nine attempts and remain in danger of relegation from the Scottish Premier League.
The visitors were on top for much of the opening half and winger David Templeton hit the outside of the post and Mehdi Taouil fired a good opportunity wide before limping off.
Hibs received a lifeline when goalkeeper Graham Stack denied Ian Black from the spot after 43 minutes after the goalkeeper had brought down Stephen Elliott following Callum Booth's short back-pass.
Hearts' pressure told when Ryan McGowan headed in after Andy Webster's effort had been saved, but the visitors conceded from the restart, Marius Zaliukas diverting Danny Galbraith's cross into his own net.
Webster then drilled in after 83 minutes and substitute Rudi Skacel struck a stoppage-time third as Hearts took victory and left Hibs manager Pat Fenlon in search of his first win as boss.
Hearts travelled across the capital with two wins and a draw from their previous three games but with December's pay outstanding - the third straight month of delayed wages.
However, now the January transfer window is open, Hearts were keen to impress.
Hibs began the better as Danny Galbraith screwed a shot wide from Leigh Griffiths' pass before Hearts' quality soon began to tell.
Lewis Stevenson was booked after nine minutes for fouling Scott Robinson, moments after another meaty tackle on Black inside the centre circle.
Paul Hanlon, left-footed and playing at right-back, was then cautioned for a mis-timed tackle on Templeton before a strong block challenge on McGowan soon after.
Templeton took on Hanlon after 16 minutes, cutting inside and leaving his marker behind before firing a vicious right-footed drive which careered off the outside of the far post.
Griffiths and Webster tangled on the edge of Hearts' box before Templeton shot wide as the visitors raced down the other end.
Taouil then missed a glorious opportunity, firing high and wide after Elliott's neat cut-back.
Taouil required treatment and limped from the field soon after, with Andrew Driver coming on.
Hibs had managed to hold firm but almost undid their good work two minutes from the interval when Booth's weak back pass failed to reach Stack and Hearts won a penalty.
Black opted to take the penalty ahead of a pleading Jamie Hamill, and Stack, who had been booked for his challenge, guessed the right way and palmed the spot-kick around the post.
Zaliukas headed wide before the break and Black had a 25-yard shot tipped over by Stack as Hearts resumed on the attack.
Webster's header from the resulting set-piece was saved, but McGowan followed up to put the visitors in front.
As Hearts players celebrated a fan in maroon from the away end was hauled away by stewards after running onto the pitch.
Hibs equalised from the restart after the ball moved left and Galbraith's cross was diverted in by Zaliukas.
Ivan Sproule was then booked for pulling down Black before John Sutton replaced Robinson as Hearts added a body up front.
And Sutton was instrumental as Hearts took the lead for the second time with seven minutes remaining.
The striker laid off McGowan's long throw for Webster to fire low into the bottom corner.
Strikers Garry O'Connor and Eoin Doyle, on for his debut, came on with four minutes remaining in place of Galbraith and Martin Scott as Hibs attempted to find a reply for a second time.
Driver was denied by a combination of Stack and Sean O'Hanlon after breaking clear before Skacel struck following Sutton's pass to seal victory.