Muhamedbegovic fizzed wide from long range on the restart before Ferguson came to his team's rescue again.
Diogo Pinto's pin-point cross found Marko Brest at the back post with his header kept out by an alert Ferguson.
Larne began to provide a threat on the counter and Mark Randall slid Sloan through but he drilled his shot wide from the edge of the box.
Olimpija finally made the breakthrough midway through the second half as substitute Durdov rose highest to power his header high into the net.
Sualehe blasted just wide as the hosts chased a second goal and their hopes of victory increased when Graham was dismissed.
But even with 10 men, the next chance fell to Larne as an unmarked Lusty found himself with just Vidovsek to beat but could only find the arms of the grateful keeper.
It was another disappointing outcome for the Irish side, who had assistant manager Gary Haveron in charge before new boss Nathan Rooney starts his reign as Tiernan Lynch's replacement against Cliftonville on Sunday.