A shot behind the two is Kiwi, Jordan Zunic, who shot a 66.
First round leader Mueck added a 68 and looked as though he would head the field going into the weekend until Geary's stunning last hole.
On the 18th he hit his drive well right then his iron shot ended up in an awkward lie at the back of the green before he chipped and holed from 25-metres.
Geary matched his opening round 66 with his collection of four birdies and an eagle in a bogey free round.
Joint-leader Mueck struggled in the hot conditions but managed to find a bit of form down the stretch to maintain his lead.
Finishing on the front nine, Mueck chipped in for birdie on the par-four seventh, bogeyed on eight then hit a sublime approach on nine to a foot from the hole for a tap-in birdie.
Mueck's playing partner, Geoff Drakeford, had the round of the day when carding a seven-under 65 to sit three shots back on 9-under par.
Drakeford got off to a slow start mixing two bogeys with two birdies on his first six holes.
A birdie on his ninth hole – the par-five 18th – sparked a resurgence and he birdied six of the nine holes on his back nine to launch himself into contention going in to the weekend.
Australian, Peter Fowler, is lurking on six-under for the tournament.