After pre-game tributes to Hughes, fatally struck while batting in a domestic game, Warner hit a first-ball boundary and he stayed positive, reaching his 10th Test hundred off just 106 balls.
In a poignant moment Warner, one of the first to rush to Hughes when he was felled last month, embraced Clarke in a long mid-pitch hug as the opener reached his century.
But shortly afterwards Clarke, who had to pass a pre-match fitness test on hamstring problems to play, went down with a recurrence of back trouble and retired hurt on 60.
Australian cricketers David Warner (left) and Michael Clarke leave the field at lunch on day 1 of the first Test match between Australia and India at the Adelaide Oval in Adelaide, Tuesday, Dec. 9, 2014. (AAP)
Australia, who won the toss, reached tea at 238 for the loss of Chris Rogers and Shane Watson, with Warner on 131 off 140 balls and Steve Smith not out 17.
Warner was at his pugnacious best, plundering 37 runs off his first 20 balls and giving Australia a positive start against the sobering backdrop of the Hughes tragedy.
There was a stirring moment when Warner looked to the heavens upon reaching 63 -- Hughes's score when he was struck -- and the crowd responded with sustained applause.
Ovation for Clarke
Clarke was also given a huge ovation as he came to the wicket, an acknowledgement of his leading role in the days after Hughes's death, in which he read a tribute at the funeral and was one of the pallbearers.
But it didn't end well for the captain, who called for the trainer after experiencing back problems and trudged off hurt with an authoritative 60 off 84 balls to his name.
Warner was out after tea when he was caught by Ishant Sharma off the bowling of Karn Sharma for 145, Australia's third wicket after they lost two in the first session.
Rogers was dismissed in the eighth over for a pedestrian nine off 22 balls when Ishant Sharma coaxed an edge to Shikhar Dhawan at second slip.
Watson followed in the 19th over, giving Dhawan his second catch in the slips off Varun Aaron and making way for Clarke to come to the wicket.
There were tributes to Hughes before the game got underway with players and fans standing and applauding in unison for a symbolic 63 seconds, and a moving welcome to country delivered by Kurna Clan man Karl Telfer.
The Australian and Indian teams, both sporting black arm bands, lined up in respect for the well-liked batsman.
Prominent broadcaster and former Australia captain Richie Benaud also narrated an emotional video shown on the ground's big screen, finishing with the words: "Forever, rest in peace, son."
Sean Abbott bowls first bouncer since Hughes death
NSW paceman Sean Abbott has claimed two wickets in his first match since delivering the bouncer that caused Phillip Hughes' death in a freak accident.
Abbott was applauded by the crowd today as he returned to the SCG two weeks after the on-field incident to bowl his first over in the Sheffield Shield match against Queensland.
He delivered a bouncer with his fifth ball.
Abbott and Mitchell Starc took two wickets each to help the Blues wrest back control of their Sheffield Shield match from Queensland, who are six for 203 in the final session day one.
The Bulls dominated the first session but lost five for 27 during the second session.
NSW players crowded around to congratulate and encourage 22-year-old Abbott after he bowled Nathan Reardon for six during his 10th over shortly after lunch.
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