Skipper Brathwaite, who took the match into a final day with a defiant overnight 101 after Australia declared their second innings at 182-2 on day four, couldn’t keep the momentum going against Lyon and was bowled for 110.
The Caribbean nation resumed on 192-3, needing to bat through 90 overs for a draw after gamely rebuffing an attack missing the injured Pat Cummins for two sessions on Saturday.
But they were all out for 333 after some plucky late resistance.
Lyon ended with 6-128, in the process surpassing India’s Ravichandran Ashwin to become the eighth-highest wicket-taker in Test history with 446.
The #MenInMaroon go down in the 1st test after taking the game into the 5th day #AUSvWI https://t.co/FRBojO8FY8
— Windies Cricket (@windiescricket) 1670137738000
“To win the first Test of any series is important. We are playing Test cricket and we expect a tough fight,” said Lyon. “I was pretty happy with that one (Brathwaite’s wicket), he’s a superstar batsman.”
It extended the West Indies’ 25-year run of failing to win a Test on Australian soil, with the hosts retaining the Frank Worrell Trophy ahead of the second, and final, Test in Adelaide starting Thursday.
Brathwaite said after his day four exploits that the opening overs would be “very, very crucial”, and in front of a spartan crowd, it was Australia who prevailed.
Kyle Mayers, who has been ruled out of any further bowling in the two-Test series with a shoulder strain, added just 10 runs to his overnight nought.
Lyon made the breakthrough, with Mayers getting a thick edge to Steve Smith at slip.
Brathwaite was almost chanceless in making his 100, but Lyon, in his 111th Test, finally beat the bat and he was bowled, ending a magnificent innings.
Part-time spinner Travis Head was brought on at the other end and in his first over accounted for Jason Holder for three, with Smith taking a spectacular slip catch.
Australia took the new ball and with it came their pace battery. Josh Hazlewood enticed an outside edge from Joshua Da Silva which Usman Khawaja collected at second slip to leave the West Indies in trouble.
But Rostan Chase and Alzarri Joseph (43) put up resistance, adding 82 runs for the eighth wicket before Head stepped up once again to end the partnership, bowling Joseph.
Lyon took his fifth to remove Chase for a battling 55 then Kemar Roach for a duck to wrap it up.
The West Indies never recovered from a dominant first innings batting display from Australia with Marnus Labuschagne and Smith both smacking double centuries to propel them to a massive 598-4 declared.
After the West Indies were removed for 283 in reply, Labuschagne then belted 104 not out to become only the eighth player to achieve the 200-100 feat in the same Test, joining the likes of Sunil Gavaskar, Brian Lara and Kumar Sangakkara.
While outplayed, a young West Indies did show grit and determination.
Few expected them to take the game to five days against the world’s top-ranked side, with their new opening partnership of Brathwaite and debutant Tagenarine Chanderpaul showing great promise, producing stands of 78 and 116.
But their bowlers let them down, taking just six wickets while conceding 780 runs.
Their stocks were, however, depleted with allrounder Raymon Reifer ruled out injured before a ball was bowled.
Top-order batsman Nkrumah Bonner suffered concussion and was substituted, Mayers was unable to bowl in the second innings with a shoulder strain and Roach limped off with a hamstring niggle.
With the injuries piling up, the West Indies sent an SOS to uncapped Marquino Mindley who is en route to Australia as cover for the Adelaide Test.