After Head smashed 119 from 134 balls to take Australia to 283 and a first-innings lead of 95, Hazlewood took four wickets for just two runs at the start of the West Indies second innings to deal a hammer blow to the visitors.
At stumps on the second day, the West Indies were 73-6, still 22 runs from making Australia bat again.
Joshua Da Silva was not out 17, with Justin Greaves dismissed off the last ball of the day’s play.
Hazlewood removed the top four West Indies batsmen in a superb spell of seam bowling.
He dismissed Tagenarine Chanderpaul for a first ball duck, then in his next over he had captain Kraigg Brathwaite caught by Head at a deepish short leg.
The West Indies were 7-3 when Alick Athanaze gloved a bouncer to keeper Alex Careythen 19-4 when Kavem Hodge edged to Steve Smith at second slip
Kirk McKenzie and Greaves tried to rebuild the innings and took the score to 40 before McKenzie tried an expansive drive off Cameron Greenonly to spoon the ball to Marnus Labuschagne at short cover.
Greaves and Da Silva batted sensibly and looked certain to take the West Indies safely to stumps, only for off-spinner Nathan Lyon to trap Greaves lbw for 24.
On a pitch that troubled every other batsman, Head seemed to be playing on a different surface when he batted, bringing up his seventh Test century with a glorious cover drive to the boundary.
He eventually fell after making a brisk century, caught brilliantly on the boundary by Kavem Hodge off the bowling of Alzarri Joseph, but by then the damage had been done and Australia were firmly in control.
The Australians were expected to dominate a below-strength West Indies, who have three players on debut in this match.
But led by exciting newcomer Shamar Joseph, the visitors took regular wickets throughout the first two sessions to initially keep the Australians on the back foot.
Joseph, playing only his sixth first class match, ended with 5-94 in a magnificent Test debut.
Australia had reshuffled their batting order on the retirement of David Warnermoving Steve Smith to opener so they could bring Green back into the side.
The first part of that experiment failed when Smith fell for 12 on Wednesday, so the Australians would have been hoping for big runs from the towering Green.
But he was gone for 14 in just the second over on Thursday morning, caught by wicketkeeper Da Silva off Shamar Joseph to leave the Australians 69-3.
Head came in and immediately looked to attack while Usman Khawaja, who started the day on 30, was slowly accumulating runs at the other end as the score passed 100.
It was another debutant, Greaves, who made the breakthrough, enticing an extravagant drive from Khawaja, who only succeeded in edging it to Athanaze at second slip.
All the batsmen struggled with the slow pace and variable bounce of the wicket, and it was no surprise when the Australians lost another wicket to the slips cordon, Mitchell Marsh edging to third slip where Greaves took a sharp catch.
Greaves nabbed his second wicket when he had Alex Carey caught by Da Silva, before Shamar Joseph got his fourth when Mitchell Starc gloved a ball to short leg.
The West Indies kept taking wickets, but they were unable to stem the runs and what could have been a manageable Australian lead quickly blew out to a daunting one.
