Five overs into the evening session, Burns repaid the selectors' decision to retain him as David Warner's opening partner when he guided a short Jomel Warrican delivery through point for three runs. He raised his bat to the crowd of more than 50,000 fans at the Melbourne Cricket Ground.
Two balls later, Khawaja — returning after missing the last two tests with a left hamstring injury — made the most of a misfield at square leg to snatch a single and complete his third century from three tests.
Steven Smith was unbeaten on 32 at stumps with Adam Voges on 10.
Burns had been regarded as a prime candidate to make way for the return of Khawaja from injury, but selectors stuck with him and instead demoted the unlucky Shaun Marsh.
He was the quiet partner as David Warner provided a trademark rapid start for Australia, which was sent in to bat as West Indies captain Jason Holder hoped his bowlers could exploit moisture in the surface from rain that delayed the start of play by an hour.
Warner stroked five boundaries in the first three overs and scored 23 off 12 balls before skying a short-pitched Jerome Taylor delivery to Marlon Samuels at extra-cover.
Burns and Khawaja shared a 258-run partnership — the highest 2nd wicket stand at the MCG for 46 years.
After working cautiously up to the lunch break, Burns and Khawaja batted more expansively from then on, confidently playing shots and taking advantage of some lackluster West Indies fielding to keep the runs flowing.
The West Indies missed an opportunity to remove Khawaja early in his innings, but the chance was dropped at gully off Taylor with the batsman on 23.
The big second-wicket stand ended when Burns was stumped on 128 coming forward to a Kraigg Braithwaite (1-31) arm ball that went past the outside edge. Burns hit 16 fours and a six in his 330-ball knock.
Holder decided to take the second new ball 10 overs before stumps and the decision soon paid dividends when Khawaja was caught behind down the leg side off Taylor (2-83) for 144. He was lucky not to have been out two overs earlier when he was dropped by Samuels at cover.
Khawaja's inclusion came at the expense of Shaun Marsh, who scored 182 runs in the opening test at Hobart, which Australia won by an innings and 212 runs.
BRIEF SCORES (FULL SCORECARD)
Australia 1st innings: 345 for 3 (Usman Khuwaja 144, Joe Burns 128; Jerome Taylor 2/83).