Hearts are still waiting to finally secure the European spot that is within their grasp for next season.
Leading by a Kevin McKenna strike at half time Hearts looked bankers to go on and win.
But an uncharacteristic win from Steven Pressley gifted Colin McMenamin the equaliser 20 minutes from time.
It was a significant strike for the Livi man as he has now netted in consecutive matches against the top three sides in Scotland - Celtic, Rangers and Hearts.
But Hearts should have had this all sewn up by half time.
Berra headed a Boyack corner wide before Maybury fired a 20 yarder just wide of the target.
McKenna broke the deadlock after 18 minutes volleying home Boyacks's corner at the back post.
But Kirk was only inches away from bending home a spectacular second and McKenzie had to look lively to smother McKenna's snap shot.
But the former Hearts keeper could only parry Neilson's cross and it took a goal line clearance from Andrews to deny McKenna.
It was ironical that Pressley had been flawless until he misdirected a header from McKenzie's long goal kick that allowed McMenamin to round Craig Gordon and score from a tight angle.
That turned the game and it took an outstanding stop from Gordon to deny Fernandez as Livingston looked likeliest winners in the dying minutes.