Put in to bat by Dinesh Chandimal, Australia amassed a world record 263 for 3, and then restricted Sri Lanka to 178 for 9 to take a 1-0 lead in the two-match series.
Maxwell, opening the batting for Australia in a T20I for the first time, destroyed the Sri Lankan bowling with an unbeaten 145 off 65 balls, studded with 14 fours and nine sixes. His blitz powered Australia past Sri Lanka's nine-year record of 260 for 6 against Kenya in 2007.
Skipper David Warner gave Australia a fiery start with 28 off 12 balls during an opening stand of 57 with Maxwell to lay the foundation.
Sachithra Senanayake, the off-spinner, bowled Warner with a looping delivery that hit off-stump, but there was no respite for Sri Lanka at the captain’s departure.
Maxwell, in his 35th T20I, found another able ally in Usman Khawaja, who scored 36 off 22 balls, as the duo added 97 for the second wicket.
Sachith Pathirana, the debutant left-arm spinner, got rid of Khawaja, but Travis Head came out to join Maxwell and the duo made merry at the packed Pallekele International Stadium.
Maxwell and Head, who scored an 18-ball 45, put on 109 for the third wicket as it rained boundaries. Maxwell fell 11 short of Aaron Finch's top T20I score of 156 as he faced only one ball in the final over of the innings.
Sri Lanka was never in the chase after losing Tillakaratne Dilshan and Kusal Perera (4), the openers, in the first two overs.
Mitchell Starc, the pace spearhead, struck in his very first over to have Dilshan, set to retire from international cricket after the second T20I, bowled for four.
A mounting asking rate was too much for the inexperienced Sri Lankan batting outfit as wickets tumbled at regular intervals. Chandimal top-scored with 58, his fourth T20 half-century, and Chamara Kapugedara smashed a 25-ball 43, studded with three fours and three sixes, to lend the total some respectability.
Starc and Scott Boland claimed three wickets each as Australia held sway from beginning to end.
The teams will now move to Colombo for the second and final T20I on September 9.