Australia couldn’t quite complete a two-day victory in Adelaide, but are unlikely to be detained long in wrapping up a win. Josh Hazlewood dismantled West Indies’ top order in ruthless style after Travis Head’s hometown century secured a handy lead on a tricky surface against a spirited visiting attack.

From what was a much even contest midway through the day, with Australia six down and still 20 behind, they pulled away as pre-series prediction had suggested they would, although with the bat were made to earn their position of strength. The game hurtled along, particularly when Head switched on the afterburners.

But though West Indies did not begin their second innings until into the last session – with Shamar Joseph completing a memorable debut by claiming a five-wicket haul – there was the looming fear about what could happen against the new ball.

And it came to pass as Hazlewood, who finished the day on 4 for 18, had taken out the top four while conceding just two runs; in fact, he had three wickets before even being scored off. He struck with his first ball of the second innings when Tagenarine Chanderpaul’s technical challenges were exposed with an edge to Alex Carey. Soon after, captain Kraigg Brathwaite could consider himself a little unfortunate when a firm clip off the pads was snapped up by Head at short leg on a day where he could do no wrong.

Alick Athanaze gloved a loose hook – and burned a review – the ball after Australia had wasted the DRS for a caught-behind appeal. Kavem Hodge, one of West Indies’ three debutants, edged a drive to second slip as the innings sank to 19 for 4.

Kirk McKenzie briefly counterattacked with some crisp strokeplay, especially through the off side, before chipping Cameron Green to cover. At that stage, 40 minutes remained in the day, and it was far from out of the question if Australia’s bowlers would rattle through the rest.

Justin Greaves, who had earlier bowled well on debut, and Joshua Da Silva, provided some resistance, only for Greaves to fall on what became the final ball of the day. Australia successfully reviewed for an lbw for Nathan Lyon, with the ball hitting leg stump from around the wicket. With West Indies still 22 behind, Pat Cummins appeared to briefly ponder asking for the extra half an hour, although there was no certainly the umpires would have granted it.

Earlier, the fact Australia had the lead they did was almost entirely down to Head. West Indies had chipped away during the morning session, and when Carey was caught behind, they still trailed. But Head sped into the 90s with a flurry of runs against Shamar Joseph, and brought up his century from 122 balls when he dispatched left-arm spinner Gudakesh Motie through the covers.

It was his first Test century since the World Test Championship final against India in June, and the first time he had passed fifty since the Headingley Test in the Ashes next month. Head had entered in just the second over of the day, and dominated on a different level to any other batter in the game. After reaching his century, he flicked the switch and carted Shamar Joseph for consecutive sixes over the leg side.

Head and Mitchell Starc added 54 for the seventh wicket to take Australia ahead. After Starc had fended Shamar Joseph to short leg, Cummins provided support in another useful stand until Head picked out deep midwicket aiming for another six.

But while the result will likely end horribly one-sided, it should not detract from the performance of Shamar Joseph, whose fifth wicket came when he speared one through Lyon with the second new ball. He walked off to a standing ovation, and gave the crowd a bow.

In his first over of the day, he was taken for consecutive boundaries by Green, but responded by finding the outside edge next ball with a perfect delivery which moved away a fraction and sent the bowler on another sprint celebration across the Adelaide Oval outfield the morning after he had become a story around the world.

Shamar and Alzarri Joseph maintained early pressure on Head and Usman Khawaja, the latter happy to bide his time but the former keen to be aggressive although not always at his most fluent. Once Green fell, West Indies quickly went to a short-ball plan against Head, although the surface did not quite have the pace in it to be hugely problematic.

Head went past 3000 Test runs with a lofted drive over the covers as the partnership started to dominate. Khawaja was shaping up well, putting a couple of pulls away strongly through midwicket, while Head also deposited Greaves into the stands over square leg.

But just as concerns were growing as to whether West Indies could maintain the pressure, the medium pace of Greaves lured Khawaja into driving a wide delivery, and the edge was well held at second slip for his first Test wicket.

Mitchell Marsh struggled early in his innings, multiple times edging short of the cordon, and had 1 off 22 balls before he laced a cover drive off Shamar Joseph. However, it wasn’t a sign of a change in fortune. After another edge fell short of third slip, and Greaves moved up even closer, wearing a helmet, and brilliantly held the opportunity off Kemar Roach.

Australia were 129 for 5 and West Indies had a glimmer of staying in the game – but a few hours later, they were just trying to make the third day.