Shehzad was unbeaten on 55 for his third fifty as Pakistan reached 116-1 at lunch on the fourth morning, stretching their lead to 267 and further press their claim for a 1-0 lead in the two-match series.
With Shehzad was first innings century-maker Younis Khan, on 26, after Pakistan had resumed on 38-0.
Pakistan had taken a big 151-run lead in the first innings after scoring 454 and dismissing Australia for 303.
Australia had looked to stop the flow of runs and had a good chance of breaking through early, but Brad Haddin failed to grasp a low catch off spinner Steve O'Keefe when Shehzad edged one on to the pads which popped out of wicketkeeper's hands.
Shehzad reached his fifty off 128 balls with a single and has so far hit four fours.
Younis hit a six off Lyon to continue the solid form he showed in the first innings when he made 106.