Fit-again Khawaja hit 144 for his third ton in four Test innings and opener Burns cracked 128 for his second Test hundred of the season as the Australians reached 345 for three at stumps after being sent into bat.
Skipper Steve Smith was unbeaten on 32 with Hobart Test double centurion Adam Voges on 10.
Before the lowest Boxing Day crowd of 53,389 at the Melbourne Cricket Ground in 16 years, Australia made Windies skipper Jason Holder pay dearly for sending the home side into bat after winning the toss.
Khawaja continued his rousing form this season after scoring 174 and 121 in the first two Tests against the Kiwis last month.
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He shared in a stand of 258 runs with Burns in the third-highest partnership for the second wicket at the famous ground.
Only two Australian partnerships for the second wicket at the MCG were higher -- Ian Chappell-Bill Lawry's 298 against the West Indies in 1968 and Don Bradman-Bill Woodfull's 274 against South Africa in 1931.
But Taylor had the last word when he snared Khawaja's wicket just two runs later when he was caught down leg-side by wicketkeeper Denesh Ramdin just under six overs from stumps.
Khawaja's runs came off 227 balls in 331 minutes with just six fours and a six.
Not since October has Khawaja been dismissed for less than 100 in any format of the game.
- Hapless tourists -
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Burns also made a personal statement with his ton amid concerns over his position in the side with the return of Khawaja.
Burns was finally out when he was smartly stumped by Ramdin off part-time spinner Kraigg Brathwaite for 128.
Burns reached the triple figures first, cracking spinner Jomel Warrican through point for three runs and Khawaja followed two balls later off a misfield at square leg for a single.
It was the second ton of the season for Burns, who scored 129 against New Zealand in Brisbane. He batted for 312 minutes and hit 16 fours and a six.
So far in the series, Australia have amassed 928 runs for the loss of just seven wickets as the home side looked to build another formidable first innings total.
The Windies removed dangerous opener David Warner cheaply for 23 in the fifth over of the innings.
Warner belted boundaries off Kemar Roach's first three balls before plundering 15 off his opening over.
But Warner was out three overs later when his attempted pull shot lobbed to Samuels, who took three snatches at the ball before holding the catch in the covers.
The West Indies last won a Test in Australia almost 18 years ago.