The dynamic opener posted his third ton of the series and 12th in Tests as he honoured the memory of his fallen friend Hughes, who was fatally struck by a bouncer at the same Sydney Cricket Ground in November.
Upon reaching the symbolic score of 63 that Hughes had made when he was hit, Warner kissed the ground and then looked skywards before clapping in tribute.
Warner scored 101 and shared in an opening stand of 200 on a benign SCG pitch with veteran Chris Rogers, who again fell short of a ton in his fifth consecutive half-century of the series.
Skipper Steve Smith and Shane Watson maintained Australia’s grip with an unbroken 144-run stand after winning the toss to put the home side at a formidable 348 for two at the close.
Smith, who glided to his half-century off 67 balls for his fifth innings beyond 50 in the series, was unbeaten on 82 with Watson on 61.
Watson was dropped by Ravichandran Ashwin at slip off the second-last ball of the day.
It is seven consecutive Tests where the in-form Smith has scored a fifty or a hundred.
India have already lost the Border-Gavaskar Trophy with Australia holding an unassailable 2-0 lead following wins in Adelaide and Brisbane.
The tourists have won only one of their last 22 Tests overseas and have been successful in only one of their 10 Tests at the Sydney Cricket Ground, that sole victory coming 37 years ago.
Warner batted for 180 minutes with 16 fours, pulling Mohammed Shami to the boundary to bring up his ton off 108 balls with 16 fours.
He was out soon after for 101 off 114 balls, caught at slip off a leading edge from spinner Ashwin.
Rogers, who gave chances on 19 and 90, followed Warner to the pavilion six balls later when he was bowled for 95 by Shami.
The Sydney Test was being played against the poignant backdrop of the tragic death of Hughes.
Warner posted his first Test century at the SCG and he, along with Smith, Watson, Brad Haddin and Nathan Lyon, were all on the field when Hughes was felled by the short-pitched ball.
A plaque honouring the batsman has been installed outside the home dressing room at the SCG and served as a reminder for the Australian players of their former team-mate.
India, with Virat Kohli leading the team after the sudden Test retirement of Mahendra Singh Dhoni, made four changes with Rohit Sharma, Suresh Raina, Wriddhiman Saha and Bhuvneshwar Kumar coming into the side.
The tourists left out opener Shikhar Dhawan with Lokesh Rahul promoted to open the innings, Sharma replacing Cheteshwar Pujara and Saha for Dhoni at wicketkeeper, while Kumar came in for paceman Ishant Sharma.
The Australians made only one change with Mitchell Starc replacing injured paceman Mitchell Johnson. (AFP)