The hosts, who have already secured the four-test series after wins in Adelaide and Brisbane, raced to 123 without loss at lunch on the first day.
The death of the 25-year-old Hughes, who was struck by a short delivery in a first class match in late November, has hung over the entire series but it has been brought to the fore at the Sydney Cricket Ground.
Cricket Australia unveiled a memorial plaque outside the home side's dressing room on Monday, while both teams paid tribute to the left-hander before the game began on Tuesday.
Regular captain Michael Clarke, who tore a hamstring in the first test and is fighting to be fit for the upcoming World Cup, also spoke at length about Hughes in a television package before play started.
"This was his ground, the Sydney Cricket Ground," Clarke said in a Nine Network tribute. "This is where he played his last game, this is where his spirit will live forever.
"The cheeky little bugger, he would be up there, smiling on us now wanting us to be happy enjoying life, getting on with it."
Rogers and Warner did exactly that after Steve Smith, Clarke's replacement as skipper, won the toss and chose to bat.
The pair were scoring at almost eight runs an over for the first 15 minutes before the run rate slowed.
Warner belted three successive boundaries off Umesh Yadav to race through the 40s before he brought up his 14th test half century in the next over.
The left-hander also kissed the pitch and signalled to the sky when he reached 63, the score Hughes was on when he was hit by the ball, and went to the break on the mark.
Rogers was on 52, his fifth successive half century and 10th overall.
Australia, who hold a 2-0 lead in the series, made one change from the drawn third test in Melbourne with pace bowler Mitchell Starc replacing Mitchell Johnson, who is resting a hamstring injury as a precaution ahead of the World Cup.
India's new captain Virat Kohli, leading the side after the surprise retirement of Mahendra Singh Dhoni, made an immediate impression with wholesale changes.
Wicketkeeper Wriddhiman Saha, who played in the Adelaide test when he replaced Dhoni, was recalled while Kohli also shook up the top order.
Opener Shikhar Dhawan and number three Cheteshwar Pujara were both dropped, with Rohit Sharma and Suresh Raina expected to move up the order, while pace bowler Ishant Sharma was replaced by Bhuvneshwar Kumar.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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