At the Gliderol Stadium, the visitors finished at 363/8 declared after 91 overs in reply to the hosts' first-day total of 219 all out.
After the Indian bowlers, led by Varun Aaron, made full use of the seamer-friendly conditions, it was the turn of their batsmen to get in some good batting practice and get versed with the conditions on offer ahead of the four-Test series starting in Brisbane on December 4.
Suresh Raina (44) and Rohit Sharma (23) were also among runs.
The day began with Vijay and Pujara at the crease and they were intent on making good use of the conditions.
They batted without any discomfort and duly notched up their half-centuries in good time, in total putting on 85 runs for the second wicket.
Both batsmen retired after getting their respective fifties.
Ajinkya Rahane (1) was the only frontline batsman to have missed out on the day, as he was dismissed by 16-year-old Sam Grimwade, thanks to a diving low catch at mid-off by Ryan Carters.
After lunch, Kohli and Raina batted with ease and pushed the score past the hosts' first innings total.
