Hearts dominated the game in terms of chances, but Hibs goalkeeper Ben Williams made a number of impressive saves to earn his side a point.
The former Crewe stopper twice did well to hold stinging efforts from John Sutton in the opening stages of the match.
Williams then denied Andy Webster's ambitious volley with a superb fingertip save on the hour mark.
Leigh Griffiths thought that he had won the game for Hibs with a superb 35-yard free kick, which hit the underside of the crossbar and then bounced well over the goal line.
However, the officials did not spot this and referee Euan Norris only awarded a corner kick as Webster headed the ball behind.
Hearts climb one place to 10th in the Scottish Premier League table, while Hibs remain sixth.