David Warner scored a brilliant 145 and dedicated it to close friend Phillip Hughes as Australia returned to Test action for the first time since their former batsman's death.
Hughes died aged 25 after being hit in a Sheffield Shield match by a bouncer from Sean Abbott - who also returned to cricket on Tuesday with two wickets against Queensland.
The Test at the Adelaide Oval was preceded by emotional tributes to Hughes and both Warner and captain Michael Clarke, along with Steve Smith, honoured their fallen team-mate with significant scores - though Clarke retired hurt after aggravating his troublesome back injury.
In pictures: Phillip Hughes funeral
Hughes was named '13th man' for the match and his Test cap number, 408, adorned both the outfield and Australia's shirts.
Prior to the start of the Test, the two teams watched a video tribute narrated by former Australia Test captain Richie Benaud before players, fans and officials applauded for 63 seconds - marking the fact Hughes was unbeaten on 63 at the time he suffered the fatal blow.
Australia won the toss and chose to bat first, and Clarke - a close friend of Hughes who delivered a touching tribute at his funeral last week - sounded in bright spirits.
Asked about the decision to name Hughes as the 13th man, he said: "We do have a 13th man and I think we will have one for the rest of our careers. Phillip Hughes is our 13th man today and he will be with us the whole way.
"I think it's going to take a long time to get over it but what I know my little buddy would like us doing is getting out here and playing some good cricket."
Virat Kohli, captaining India for the first time in Tests, added: "It's been a sad time but this is the only thing that can heal it."
Recalling his own memories of Hughes, he added: "He was one of the guys I spoke to more than anyone. Surprisingly, or coincidentally, he asked me for my bat in Jaipur in the last home series we played, the one-day series, and I wish I'd given it to him.
"He was a lovely chap, very cheerful. I knew him well."
The Test match was originally due to start last Thursday but was delayed with Hughes' funeral taking place on Wednesday.
Warner seemed to channel his emotions into his batting as he piled on the runs early on - making 35 off the first 17 balls he faced.
The first short ball of the game came in the fourth over, bowled by Mohammed Shami at Warner and applauded by the crowd.
Once Australia reached 50 they lost their first wicket as Chris Rogers was tempted by a teasing delivery from Ishant Sharma and was caught by Shikhar Dhawan for nine.
Shane Watson came in and immediately faced a big bouncer from Ishant Sharma but the fireworks continued to come at the other end, where Warner soon reached 50 and marked it by raising his bat to the heavens in tribute to Hughes.
Watson, however, was soon out, becoming Dhawan's second victim at second slip when he nicked a Varun Aaron delivery.
That brought Clarke out to the middle, and he received a huge ovation after a difficult week.
And the crowd were once more on their feet when a sweep shot took Warner to 63 and he again stopped to acknowledge Hughes.
In the 37th over, Warner eased the ball through the covers for a single which brought up his century, marked with a further skyward salute and a lengthy embrace with Clarke.
The captain had been making solid progress himself, but the mood suddenly changed when, without warning, he appeared to suffer a back spasm when adjusting against a wayward delivery from Ishant Sharma.
He immediately began stretching and received treatment on the pitch, but retired hurt for 60 without facing another ball and went to hospital for scans - a sad way to end such an emotional innings.
After that significant loss, Warner kept the scoreboard ticking over. He survived a review when India thought they had him stumped while on 133, but the tourists did not need to wait much longer.
Having hit 19 fours, Warner went looking for a first six but succeeded only in finding Ishant Sharma on the boundary, giving Karn Sharma his first Test wicket as the batsman went for 145.
Smith had quietly established himself and on two occasions both he and Mitchell Marsh hit fours in the same Karn Sharma over, before a Smith boundary off Aaron took Australia past 300.
Smith - who batted in a cap rather than a helmet when spinners Karn Sharma and Murali Vijay bowled in tandem - reached 50 with a single off Karn Sharma and then 63 with a boundary off Ishant Sharma, saluting Hughes on both occasions.
Marsh fell for 41, Kohli with the catch at slip off Aaron, and Mohammed Shami picked up the wickets of nightwatchman Nathan Lyon for three and wicketkeeper Brad Haddin for a duck as India finished the day strongly with the new ball.
That left Australia 354 for six at stumps, with Smith unbeaten on 72.