Hearts claimed a third straight Edinburgh derby win of the season as Hibernian's long wait for victory against their city rivals continued.
Hibs goalkeeper Graham Stack saved an Andy Webster header before Craig Beattie's deft control and finish put Hearts ahead in the 28th minute.
The visitors' best chance fell to Roy O'Donovan, whose header was saved by Jamie MacDonald.
Suso Santana's solo goal sealed Hearts win in injury time.
With Hearts on course to finish in the Scottish Premier League's top six and Hibs second bottom of the table, the two sides' next meeting on league business is likely to be next season.
However, Pat Fenlon's side may get a chance to end their near three-year winless streak in the derby in the Scottish Cup, with a final match-up of the capital sides still possible.
An early clash of heads between Hibs' George Francomb and Hearts' Rudi Skacel resulted in the former being replaced by Matt Doherty.
Webster's header off Ian Black's corner was superbly saved by goalkeeper Graham Stack.
Hibs responded with a quick break on the left but Pa Saikou Kujabi's teasing low centre found no takers.
And, within minutes, Hearts were ahead as Black's long diagonal found Beattie bearing down on goal and the striker took a touch on the run before rolling the ball past the advancing Stack.
Beattie volleyed over before Hearts were forced into a change of their own, with Stephen Elliott unable to recover from a collision with Stack and making way for Scott Robinson.
David Wotherspoon's dangerous free-kick was beaten away by Hearts keeper Jamie MacDonald in the opening minutes of the second half.
Beattie exhibited his defensive qualities with two important clearances from Doherty headers as Hibs continued to threaten at set pieces.
Striker Leigh Griffiths drifted wide to cross for O'Donovan to nod towards goal but MacDonald was out quickly to make the block.
Substitute Garry O'Connor's free-kick rebounded off the Hearts wall to Lewis Stevenson, who made a good connection but ended up disappointed as his effort swerved wide.
Suso, who had replaced Skacel, doubled Hearts lead after picking up the ball just inside the Hibs half and weaving his way down the left before cutting inside and curling the ball past Stack.