Warner's whirlwind unbeaten 100 from 56 balls on Sunday at Adelaide Oval underpinned Australia's 2-233 - the nation's fourth-highest T20 total and best on home soil.
In reply, Sri Lanka stumbled to 9-99 as Australia emphatically took a 1-0 lead in the three-game series in front of a crowd of 16,268.
The winning margin is, by runs, the third-largest in a T20 international between Test nations - Pakistan's 143-run victory against the West Indies last year is the biggest.
Warner, on his 33rd birthday and in his first home international since being banned for ball tampering, leapt wildly into the air on reaching his milestone from the last ball of Australia's innings.
The left-hander, with support from captain Aaron Finch (64 from 36 balls) and Glenn Maxwell (62 from 28), savaged Sri Lanka's bowling.
The trio made a mess of wayward quick Kasun Rajitha, who finished with 0-75 - the most runs conceded in a four-over spell in T20 internationals.
Warner's ton featured 10 fours and four sixes, surpassing his previous best T20 international score of 90 not out.
He's the fourth Australian to hit a T20 international century, after Maxwell (three times), Finch (two) and Shane Watson (one).
Warner set a rampant tone with Finch in a opening partnership of 122 runs from just 10.5 overs.
The pair reached their half-centuries in the same over, both by smacking consecutive sixes from the hapless Rajitha.
After the dismissal of Finch (eight fours, three sixes), Maxwell (seven fours, three sixes) produced a daring knock before a crowd of 16,268.
Maxwell and Warner put on 107 runs and their century stand took only 52 balls.
Sri Lanka's run chase was cruelled by early wickets: they were in tatters at 3-13 after 22 balls.
Australian pacemen Mitchell Starc (2-18) struck in the first over and Pat Cummins (2-27) was on a hat-trick in the fourth over but was denied the rare feat.
Spinners Adam Zampa (3-14) and Ashton Agar (1-13) were also wicket-takers as Dasun Shanaka top-scored with 17.
The series continues on Wednesday in Brisbane with the last game on Friday in Melbourne.
Australia will host Pakistan in a three-match T20 series on November 3, 5 and 8.