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Charles, coming off his maiden one-day international century, struck 57 off 35 balls to propel the tourists to an imposing first innings total of 191 after captain Darren Sammy won the toss and elected to bat at the Gabba.
Australia's Adam Voges blasted a swashbuckling 51 off 33 balls to give them hope of hauling in the total, but paceman Kieron Pollard and spinner Sunil Narine combined for five quick wickets to make sure the hosts' chase came to a crashing halt.
The emphatic victory against a second-string Australia side ensured West Indies finished their tour Down Under on a high, having dismally surrendered the preceding one-day series 5-0.
"Obviously, it's a bit too late ... We are world (Twenty20) champions so we had to play like that," man-of-the-match Pollard said in a televised interview after rattling through Australia's middle order to take 3-30.
"We had a good score on the board and we just had to try to defend it."
Australia brought a depleted lineup to the Gabba, with a number of first-choice players having headed to India early to prepare for a four-test series.
The rawness showed as Charles, Darren Bravo (32) and Pollard (26) flayed the Australian pacemen to drive West Indies past 100 within the 12th over, before Sammy chipped in with a useful seven-ball cameo of 20 late in the innings.
After the early loss of opener Aaron Finch for four, Australia appeared to be sailing toward victory before sharp work by wicketkeeper Devon Thomas saw Shaun Marsh (21) and Voges run out in three balls.
The run-outs proved a turning point, as spinner Narine soon coaxed a miscued sweep shot from captain George Bailey, the top edge well caught by a lunging Narsingh Deonarine.
Pollard then used the slower ball to devastating effect to have wicketkeeper Brad Haddin, debutant Ben Rohrer and all rounder James Faulkner all caught slogging.
Paceman Nathan Coulter-Nile belted a couple of late sixes in an unbeaten 16 but it was all just entertainment for the crowd as West Indies closed out a comfortable victory.