Maxwell blasted an unbeaten 120 from 55 balls, propelling Australia to 4-241, the highest T20I innings score at Adelaide Oval.
Coming in at No.4, Maxwell registered his century from just 50 balls - two balls quicker than the previous best in a T20I in Australia.
South African Rilee Rossouw scored a T20 ton from 52 balls against Bangladesh during the 2022 World Cup.
Maxwell equalled Indian great Rohit Sharma with the most T20I centuries - five - with his extraordinary knock.
The Victorian belted eight sixes and 12 fours to set Australia on course for victory in game two of the three-match series.
Maxwell tore the attack apart after Australia made a wobbly start. (Matt Turner/AAP PHOTOS)
Australia arrived in Adelaide with a 1-0 lead after an 11-run win in Hobart last Friday night.
Maxwell's knock was a classic counter-punch, reviving Australia from a wobbly 3-64 in the seventh over.
Opener Josh Inglish (four) was caught on the square leg boundary in the second over before captain Mitchell Marsh produced an aggressive cameo.
Marsh struck two sixes and three fours, racing to 29 from his first 11 balls.
But the skipper was out on his next delivery when he attempted to loft over the leg-side but skied a high ball which Jason Holder, tracking back from mid-on, clasped after a bobble.
West Indies will have been hopeful after Jason Holder (l) removed Josh Inglis in the second over. (Matt Turner/AAP PHOTOS)
Opener David Warner (22 from 19) departed in the following over, launching at a fullish Romario Shepherd delivery but miscuing to Sherfane Rutherford at mid-off.
Maxwell then dominated an 82-run stand in seven overs with Marcus Stoinis (16 from 15) in daring fashion, posting his half-century from only 25 balls and keeping that pace to reach his century from 50 deliveries.
The 35-year-old Maxwell, Aaron Finch and Inglis share the Australian record for fastest T20I centuries - 47 balls.
Australia handed Spencer Johnson a home international debut, replacing the injured Sean Abbott.
Abbott has suffered a shoulder injury and will be replaced in Australia's squad for the final fixture in Perth on Tuesday night by fellow paceman Xavier Bartlett.