Forced to retire hurt from a toe-crushing Mitchell Starc yorker the previous evening, Joseph bounced back to claim six wickets in a session and 7-68 overall to help West Indies sensationally dismiss Australia for 207 in pursuit of their modest target of 216.
Australia's new opener Steve Smith, who made 91 not out, farmed the strike to protect Josh Hazlewood (0) when the test hung in the balance, but it was to no avail.
Joseph, playing his first test series, sent Hazlewood's off-stump flying and he dashed off across the Gabba field with his tongue hanging out before celebrating with his teammates.
"Tears would have come to my eyes but I already cried when I got my five-wicket haul," said Joseph, who was named both Man of the Match and Man of the Series.
"It's just happiness, when was the last time we won in Australia? I can't even remember. Today's a big day for us."
It was Australia's first loss in 12 pink ball tests.
The West Indies, who arrived in Australia with a weakened and inexperienced squad, were given little hope of getting anything out of the series, a judgement apparently vindicated when they lost the first test by 10 wickets in Adelaide.
"I feel like we win the series even though it's 1-1," Joseph added. "It's really amazing for my teammates, I must give another shout out to them. They're really encouraging."
Australia skipper Pat Cummins had courageously declared at 289-9 with his side still behind the visitors' first innings total of 311 before his bowlers dismissed West Indies for 193 in their second dig.
Cummins, who led Australia to a World Test Championship triumph last year, said he was disappointed at the defeat but paid full tribute to West Indies.
"That was a fantastic test match and a fantastic series," he said.
"I thought in particular, Shamar, the way he bowled today was right up there and unfortunately we weren't good enough.
"We've all played enough to know that this game humbles you pretty quickly when you're thinking you're on top of the world."
PAIN FROM INJURY
Joseph, who lit up the first test with a five-wicket haul on debut and handy runs from number 11, was unable to finish his batting innings on Saturday night, such was the pain from his injury.
He said he was in such discomfort that he almost did not turn up at the ground for day four. But some medical treatment did the trick, and he was soon bowling over Cameron Green (42) and Travis Head in consecutive deliveries.
Mitchell Marsh (10) fell next, juggled between the slipsmen, and Alex Carey (2) soon had his stumps rattled as Joseph's fiery afternoon rampage continued.
Resuming from 33 overnight, Smith continued to accumulate while Starc opted for aggression, blasting a 14-ball 21 before presenting debutant Kevin Sinclair at backward point his third catch for the game.
Cummins, caught-behind, added two before becoming Joseph's sixth victim in a lionhearted 11 over spell, which reduced the hosts to 187-8 at the long break.
Alzarri Joseph captured Nathan Lyon's bottom-edge one ball after spilling a caught-and-bowled chance to have Australia nine down and trailing by 21, setting the stage for Shamar Joseph's dramatic dismissal of Hazlewood.
West Indies last defeated Australia in a test in 2003 at Antigua.
"My message to the group is this is the beginning. It's amazing, we will enjoy it but this has to continue," said West Indies captain Kraigg Brathwaite.
"Very proud of the guys, they showed a lot of heart, especially after the first test."
