Having recovered from a hamstring strain, Khawaja celebrated his recall with a glittering 144, with Queensland team mate Burns making 128 in front of a festive Melbourne Cricket Ground crowd to drive Australia to 345-3 at stumps.
The pair's 258-run stand remained unbroken until well into the final session, with captain Steve Smith (32 not out) and Adam Voges (10) untested during the final overs.
After a run of modest scores, Burns was widely tipped to make way for the returning Khawaja but it was middle order batter Shaun Marsh making way for the stylish left-hander.
"It was just a nice feeling to make a 100 for Australia on Boxing Day," Burns told reporters.
"Certainly something to savour ... Hopefully we can go on and win the test match and win the series."
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Australia won the opener emphatically in Hobart and took a big stride toward sealing the three-match series with a game in hand after being sent in to bat by West Indies captain Jason Holder.
Holder's decision was a poor one in hindsight, with the green-tinged MCG pitch flattening out in bright sunshine after rain held up play for an hour.
His players again failed to rally, however, with the bowling tepid at best and fielding at times abysmal.
Khawaja was dropped on 23 shortly after lunch after nicking a half-chance to the gully and spooned the simplest of chances to Marlon Samuels at cover to again be reprieved on 142.
He and Burns came together early after opener David Warner was dismissed for a quickfire 23 and they erased any lingering confidence the Caribbeans nursed after their innings and 212-run thrashing in Hobart.
Unbeaten at tea, Burns and Khawaja ramped up their attack in the final session and raced to reach their centuries.
Burns made his ton and second test century first with a punch for three through point.
Khawaja followed two balls later, scrambling for a single presented by a misfield.
The pair ploughed on steadily to guide Australia past 250, with their opponents' hopes seemingly fixed on the batsmen suffering a lapse in concentration rather than succumbing to any sustained pressure.
As it happened, Burns duly delivered after the drinks break, getting stumped after charging down the wicket at part-time spinner Kraigg Brathwaite.
Khawaja appeared to succumb to fatigue rather than the bowler's guile as he tickled Taylor down the leg-side to be caught behind.
Kraigg Brathwaite said it was a "decent day" for the tourists.
"Obviously (have to) try to be build some pressure to not let them score so freely," said the spinner.
(Editing by Amlan Chakraborty)
