Despite a 45 second lead in this game, The Thistle laboured throughout the contest and almost came away with nothing.
The hosts rallied well after conceding the early goal and deserved to get back into the match before the break.
Into the second half, Knox added to his first goal, with a fine Bauros pass, before Dunedin blasted the equaliser with a perfect 30 yard freekick.
A defensive blunder in extra time saw the hosts take the advantage, before Robb converted following fine personal play with only minutes remaining.
The penalty shootout was again impressive, with Thistle eventually winning 6-5, with Simpson saving and then converting to take the visitors into the Fourth Round.
Walker, Knox, Robb, Greig and Ferguson also converted their shootout efforts.