Steven Pressley and John McGlynn jointly took the role of care taker managers for the final two games of the season.
Basel started well into the game and their striker Christian Giménez slashed a hard shot towards the far corner of the goal in the opening minutes, which needed a good save from keeper Craig Gordon.
The home team were now forced to be more committed with their attacks and they put Hearts under increased pressure, responding well to the conceded goal.
Basel's head-coach Christian Gross changed his attackers midway through the second half and his substitutions quickly paid out.
Hearts' last-gasp winner, in the 89th minute, was more a speculative attack and was made only to relieve the defensive pressure, but it paid off as Robbie Neilson pushed his shot under the body of goalie Zuberbühler with only seconds left on the clock, his first ever goal for the club.