Marcus Harris started fluently in the morning hitting boundaries at will.
But his partner Khawaja perished while going for one shot too many, giving Kuldeep his first wicket of the match.
After completing a stroke-filled half-century, Harris played on off the bowling of Jadeja to leave the visitors 128/2.
Shaun Marsh didn't last long as he edged to Ajinkya Rahane in the slips, again of Jadeja.
Shami joined the party getting Labuschagne caught at short mid-wicket where Rahane took an excellent diving catch.
Kuldeep then wove his magic around Travis Head who offered a simple return catch to the bowler on 20.
Captain Tim Paine was bowled through the gate soon after by Kuldeep leaving the hosts at a precarious 198/6.
However, rain arrived to rescue the Australians as Stumps were declared 16.3 over earlier.