Stokes launched a blistering attack after the controversial dismissal of Jonny Bairstow, (33) smiting nine sixes and nine fours to raise hopes of a repeat of his brilliant match-winning knock against the Australians at Headingley four years ago.
But with 70 runs needed for victory, he skied Josh Hazlewood (32) to wicketkeeper Alex Carey, (31) who had earlier riled him by stumping Bairstow for 10 after the batsman left his crease at the end of an over.
The crowd booed loudly and Stokes responded by striking three sixes in an over off Cameron Green (24) to reach his century and was unbeaten on 108 at lunch with England needing another 128 to level the series.
He continued the assault after the interval by clubbing Hazlewood for six and was dropped by Steve Smith (34) at deep square leg, the crowd roaring with delight when the former Australia captain - usually one of the safest pairs of hands - let the ball slip out of his grasp.
Stokes welcomed Mitchell Starc (33) back into the attack with two more maximums as he and Stuart Broad (37) shared a century partnership for the seventh wicket, the latter contributing 11.
The England fast bowler played a key role as the drama grew, surviving a series of short-pitched deliveries and trying to rile Carey at every opportunity by holding his bat in the crease at the end of the over and staring intently at the stumps.
Stokes dabbed Green for two to pass 150 off 197 balls before attempting to clear the ropes again and giving Carey a simple catch before leaving the arena to a standing ovation.
Australia's relief was palpable and the end came quickly.
Ollie Robinson (29) was caught by Smith off Pat Cummins (30) for one, and Broad's long vigil ended when he was pouched in the deep by Green off Hazlewood for 11.
Josh Tongue (25) and James Anderson (40) gamely added an unlikely 27 runs, but Hazlewood bowled the former for 19 to dismiss England for 327 and seal victory for the Australians who celebrated gleefully as they walked off to more boos from the crowd at the home of cricket.
Ben Duckett (28) earlier contributed a polished 83, sharing an excellent partnership of 132 with Stokes to drag England back into the match after they had slumped to 45-4 on Saturday.
After two pulsating matches, Australia have a firm grip on the Ashes with England needing to win the remaining three games of the series to take back the urn.
The third test at Headingley starts on Thursday.
