Australia hold a 1-0 lead in the three-Test series, having thumped the visitors by an innings and 212 runs in Hobart.
Predictions of another lopsided contest look set to be proven true.
However, in a sign of the side's high standards both centurions lamented losing their wicket in the final session.
"It's always a nice feeling to have a hundred next to your name but the disappointing thing is both of us couldn't go on and get even bigger scores," Burns said.
"My job is to do that week in, week out.
"The game is very challenging, you have to work hard every single day and that's what I'll try and do."
Burns insisted the selection showdown that hung over the squad since the first Test did not bother him.
"I never really sat down and worried about if I was going to get picked or not," he said.
"It was nice to have a week at home with the Brisbane Heat and nice to have the distraction of Christmas.
"There are always going to be nerves there but that's because you want to do well."
Brathwaite, who had Burns stumped in the 74th over, was a picture of positivity.
"It was a decent day for us," he said.
"The bowlers put in a better effort than the first Test and it's key to come tomorrow and start well again."
At Bellerive, Australia at least slipped to 3-121 prior to amassing 4(dec)-583 in their only innings.
In Melbourne, David Warner's slapdash dismissal on 23 was the only moment of early joy for the tourists.
Warner set the tone for the day, with Kemar Roach dragged out of the attack after the pugnacious opener hammered 15 runs off his first over.
Roach did not bowl in the final session.
Australia's run-rate dipped after Marlon Samuels held a juggling catch to dismiss Warner.
However, Burns and Khawaja were able to ease their way into proceedings.
Jerome Taylor handed them a bonus run in the morning session, opting to casually stop the ball with his foot at fine leg.
"Early on it was quite tough to bat out there, misfields or not," Khawaja said.
Khawaja tellingly brought up his ton by scampering through for a single after a misfield, while Burns reached three figures in the same over.
-AAP
