Australia 283 (Head 119, S Joseph 5-94) and 26 for 0 beat West Indies 188 (McKenzie 50, Cummins 4-41, Hazlewood 4-44) and 120 (Hazlewood 5-35) by 10 wickets
Australia wrapped up a 10-wicket victory before lunch on the third day in Adelaide as Josh Hazlewood claimed career-best match figures, but there was late drama when Shamar Joseph drew blood from Usman Khawaja with a bouncer when the scores were level, forcing him to retire hurt.
Shamar Joseph again showed his batting prowess at No. 11, which will surely mean a promotion in the near future, as he and Kemar Roach added 26 for the last wicket to follow the 55 they put on in the first innings.
It meant a brief second innings for Khawaja and Steven Smith. Oddly, Shamar Joseph, who claimed Smith with his first ball in Test cricket, was not given the new ball. He was eventually introduced in the fifth over with 14 needed and after being cut to the boundary first ball by Khawaja produced a lovely delivery beat Smith's edge
Then came a lifter that beat Khawaja before an awkward bouncer clattered into his helmet around the jaw area as he tried to sway out of the line. Khawaja had blood coming from his mouth and after a few moments left the field leaving Marnus Labuschagne to hit the winning runs. In more ways than one, Shamar Joseph had left an indelible mark on his debut
West Indies had resumed 22 behind with four wickets in hand after losing Justin Greaves to the final ball of the second day. They whittled the deficit down to 11 before Joshua Da Silva gave his innings away by falling for the well-telegraphed short-ball plan, top-edging a hook to deep backward square off Mitchell Starc.
Alzarri Joseph showed a solid technique and played a brace of strong cover drives against Starc but got a thin edge from around the wicket. When Gudakesh Motie became Hazlewood's fifth wicket, shouldering arms to one that was far too tight to leave, West Indies were still a run behind.
However, that lasted just one more delivery as Shamar Joseph played a first-ball cover drive that would have pleased a top-order player, bringing huge cheers from a healthy crowd who had flocked in despite the risk of very little cricket.
Each run added by the last-wicket pair was greeted by warm applause, while it added to Australia's recent difficulties over getting through lower-order stands. The return of Nathan Lyon, who had started the day bowling a single delivery, ended the resistance when Shamar Joseph charged and missed.
The second Test begins in Brisbane on January 25 and will be a day-night encounter.
