England, with six wickets in hand, needed 178 runs to win the maiden day-night Ashes test and level the series at 1-1 but fell well short of their victory target and will head to Perth 2-0 down with three matches to play.
Left-arm quick Mitchell Starc mopped up the tail to take five for 88, his eighth five-wicket haul in tests, but Hazlewood will also share the plaudits after his early intervention.
The paceman delivered a hefty blow when he removed Chris Woakes with the second ball of the day and two overs later landed a knockout punch when he had Joe Root caught behind before the England captain could add to his overnight 67.
"I didn't think it would happen that quickly. To get those early two (wickets), especially Joe Root, really set us up for the day," said Hazlewood.
"Look forward to Perth now and get ready for that."
Root's innings was always going to be crucial to his team's chances of chasing down a record 354 at Adelaide Oval and although the innings limped on into a second hour, the hope raised among the English on Tuesday was gone.
The dismissal of Woakes had an element of fortune in that the feather the nightwatchman got on the ball was picked up by snicko but not the hotspot when it was referred.
Root, however, simply walked from the field after edging behind.
The 26-year-old Yorkshireman got late to a good length delivery from Hazlewood and the ball nicked off his bat into the welcoming gloves of Tim Paine.
All-rounder Moeen Ali, who made two off 20 balls, used up England's last DRS referral when he attempted a sweep off Nathan Lyon with the ball-tracking only confirming the umpire's lbw decision.
Australia were now into the England tail and Craig Overton (7) departed plumb lbw to the first delivery with the new pink ball, an inswinger from Starc.
Starc then removed Stuart Broad caught behind and finished the job by bowling Jonny Bairstow, England's last recognisable batsman, for 36 and the tourists were all out for 233.
"Disappointing," said Root. "I don't think we did ourselves justice. We're still massively in the series. We showed that from the way we played yesterday."
Australia captain Steve Smith had been relying on his bowlers to save his embarrassment after he failed to enforce the follow-on and England's bowlers got them back into the game.
The hosts got 442-8 declared on the back of Man of the Match Shaun Marsh's 126 not out before dismissing England for 227 but Smith sent his batsmen back in only for James Anderson and Woakes to bowl them out for 138.
Only one captain in the long history of test cricket had previously lost a test after opting not to enforce the follow-on and Smith was grateful to his bowlers for getting him out of a hole.
Adelaide TestAshes 2017australiaEnglandJoe RootJonny BairstowJosh HazlewoodMitchell StarcNathan Lyon
First Published: December 6, 2017, 11:43 AM IST