Jamie Walker scored his 50th goal for runaway Scottish Championship leaders Hearts to deny Morton a shock victory on their first visit to Tynecastle since 1988.
Walker headed home with 19 minutes remaining to cancel out Craig McGuffie's opener as the match finished 1-1.
Hearts, boasting a 13-point lead at the summit, were quickly on the front foot against a Morton side without a win in seven games and Aaron McEneff drew a good save out of visiting goalkeeper Aidan McAdamas inside five minutes.
Michael Smith and Andy Halliday also went close for the hosts before Liam Boyce, the division's leading scorer, hit the Morton bar in the 36th minute with a volley off his heel.
Morton weathered the storm though and, having also hit the bar through Aidan Nesbitt's cross-shot before the break, they took a surprise lead in the 52nd minute when McGuffie fired low past Craig Gordon.
Hearts boss Robbie Neilson rang the changes soon after and the move paid dividends in the 71st minute as the two substitutes combined to draw the hosts level, Walker nodding in Armand Gnanduillet's cross.
Buoyed by that goal, Hearts pushed for a late winner but Craig Halkett and Smith could not make the most of their opportunities as the points were shared.
