The tourists – bowled out for just 43 on day one of the first Test in Antigua – trail by 301 runs after slipping to 62 for six in their second innings.
The Windies, led by Brathwaite’s seventh Test hundred, were in complete control at North Sound and secured a 363-run first innings advantage, before their attack quickly set about completing the job.
Pace bowler Gabriel had Tamim Iqbal caught by Shai Hope off the fourth delivery of the third over, before bowling Mominul Haque for a duck two balls later.
Kemar Roach, who wrecked Bangladesh in the first innings with five wickets in 12 deliveries, did not take to the field in the second because of a hamstring injury.
His absence mattered little though as their opponents offered limited resistance, home captain Jason Holder removing Liton Das to leave them struggling on 16 for three.
Gabriel continued the demolition, removing Mushfiqur Rahim and captain Shakib Al Hasan as he posted figures of four for 36, before Holder claimed Thursday’s final wicket by dismissing Mehidy Hasan Miraz.
Earlier, Brathwaite had begun slowly, adding only 33 runs in the opening two hours of play which saw him reach his landmark with one of 11 fours.
Nightwatchman Devendra Bishoo was the first casualty of the day when he has bowled by Kamrul Islam, before Brathwaite was caught by Miraz off Shakib in the first over of the second session having hit 121.
Roston Chase, trapped lbw for two by off-spinner Miraz, and Shane Dowrich, caught by Das at short-leg off Shakib, then fell in relatively quick succession as Bangladesh’s bowlers enjoyed some success.
Hope, however, added to their misery with a fine 67 which lifted the hosts to a commanding 406.
The tourists trounced England by eight wickets at Old Trafford, and can therefore wrap up the three-match series in Cardiff on Friday evening.
A match notable for England’s travails against the spin of Kuldeep Yadav also featured a minor fracas between Willey and Kumar.
The England all-rounder described the incident as “something and nothing” – but having waved Kumar away in Manchester, wondered out loud whether it was right for the seamer to twice pull out of his action while he legitimately moved in his crease 22 yards away.
“I’m guessing – but I think he was looking to see what I was going to do,” he said.
“I’m not sure what the rules are on that. I don’t particularly like it – I don’t think it is necessarily in the spirit of Cricket.
“Personally I don’t think I’d do that. I don’t think it is great.”
Willey is no shrinking presence in the middle, and he said: “I don’t mind a bit of confrontation.
“If it comes my way I am quite happy to get involved (but) we are advised to play Cricket and leave those antics to other people.”
After being flummoxed by Kuldeep’s left-arm wrist-spin, England perhaps have more pressing concerns than an occasional phantom delivery.
Jonny Bairstow and Joe Root were both stumped for golden ducks, as England lost three wickets in four balls.
Willey suspects, however, that a little more familiarity with Kuldeep will work in their favour.
“People come in, a little bit of unknown, you’re maybe not 100 per cent sure how someone’s going to bowl,” he said.
“It can baffle you a little bit. But our numbers against spin are brilliant, unbelievable, and we’ll come back.
“No doubt tomorrow will be a different outcome. It was just one of them days, someone took a few wickets.”
England will not waste undue energy fretting.
“We don’t get het-up on one little thing like that,” said Willey. “Yes, it cost us in that last game, but we don’t dwell on things like that.
“We go out and we play our way, and everyone has full confidence in our batters that tomorrow will be a different story.”
Australia were never in the hunt to haul in world No1 Pakistan’s impressive total of 194 for 7 in the T20I in Harare on Thursday, with the world No2 Ozzies reaching just 149 for 7 off their 20 overs.
The only batsmen to shine for the Aussies was wicket-keeper Alex Carey with a face-saving 37 from 24 balls. Record century-maker on Tuesday, Aaron Finch, went for just 16 while fellow opener Darcy Short struggled to 28 off a glacial 34 balls.
Best with the ball for Pakistan was Shaheen Afridi who took the wickets of Finch, Short and the dangerous Glenn Maxwell for 37 off his four overs.
Earlier some big hitting off the last two overs, accumulating 35 runs, helped Pakistan set a challenging target of 195.
Top scorer for Pakistan was Fakhar Zaman, who knocked up a blistering 73 off just 42 balls at the top of the innings. Asif Ali also contributed a quick fire 35 off just 18 balls at the death.
Standouts with the ball for Australia were Andrew Tye who took 35 for 3 from his four overs and Jhye Richardson who took 43 for 2 from his full complement.
Earlier Australia won the toss and decided to bowl in cloudy conditions with the world No1 ranking on the line.
Check out the full score card below.
Australia XI: Aaron Finch (c), D’Arcy Short, Travis Head, Glenn Maxwell, Nic Maddinson, Marcus Stoinis, Alex Carey (wk), Ashton Agar, Andrew Tye, Jhye Richardson, Billy Stanlake
Pakistan XI: Fakhar Zaman, Haris Sohail, Hussain Talat, Shoaib Malik, Sarfraz Ahmed (c/wk), Asif Ali, Faheem Ashraf, Shadab Khan, Mohammad Amir, Usman Khan, Shaheen Afridi