Peaking at around 150kmh, Joseph immediately found life with an old pink ball that had earlier caused Australia’s batters few troubles.
He bowled Cameron Green (42) and Travis Head with consecutive balls to begin the collapse.
Head’s golden duck was his third-straight in tests at the Gabba as he became just the seventh Australian to register a king pair.
Smith survived the hat-trick ball but Mitchell Marsh (10) didn’t last much longer, while Alex Carey (two) was Joseph’s fourth victim in a manic six-over spell that also cost 45 runs.
He wasn’t done though, with Starc (21 off 14) becoming Joseph’s fifth scalp inside seven overs to end a brief cameo from the Australian quick that featured four boundaries.
Australia still needed 45 to win when skipper Pat Cummins, who blazed an unbeaten career-best 64 in the first innings before declaring 22 short of West Indies’ first-innings 311, strode to the crease 10 minutes before the tea break.
He was caught behind for just three, Nathan Lyon then surviving until the interval with Australia still requiring 29 to win and complete a 5-0 summer sweep.
Lyon fell in the first over after the resumption, but Smith continued to counter-attack as he spectacularly ramped a six as the target went into single figures.
But he exposed Hazlewood once too often and Joseph clattered the stumps once more to cap an incredible solo performance.
Joseph said he thought he’d struggle to even be at the ground after being forced to retire hurt on Saturday night, until chatting to the team doctor.
“He did something to my toe, I don’t know what he did,” Joseph said.
“I feel that we’ve won the series, even though it’s 1-1.
“I already cried after my five-wicket haul ... I’m not that tired; I told my skipper today I’d bowl today until the last wicket fell.”
