jubilation of the Australians.
Root was rapped on the knee roll of his pad but surprisingly did not seek a review given the vital importance of his wicket.
Hazlewood, who removed Cook and James Vince late on Saturday’s third day, finished with three for 46 off 16 overs.
“Obviously very disappointed,” England all-rounder Moeen Ali said. “I thought the first three days we played well and we were in the game and then today we let ourselves down with the bat especially, we got in and never really got on to get that score that we needed.”
Off-spinner Nathan Lyon started the ball rolling for the Australians on day four when he dismissed in-form opener Mark Stoneman (27) and Dawid Malan (4), both caught by Steve Smith at slip.
Lyon also removed Moeen with a contentious stumping by wicketkeeper Tim Paine for 40. The TV umpire needed repeated replays before deciding that the Englishman’s back foot was not behind the crease.
Lyon finished with three for 67 and has now taken 274 wickets in 70 Tests, the highest number of wickets by an Australian off-spinner.
Starc chipped in with the wickets of Jonny Bairstow, Chris Woakes (17) and Stuart Broad to finish with three for 51.
Bairstow hit 42 off 75 balls before he ramped one over the slips and gave a regulation catch to Peter Handscomb at third man.
Broad was out caught behind for two to a faint speck detected on the infrared “Hot Spot” technology on review, while Woakes was Smith’s fourth catch of the innings.
The third paceman Pat Cummins mopped up the England innings when he had Jake Ball caught behind off a vicious short ball for one.
Australia have a formidable record at the Gabba, where they have not lost a Test match since falling to Viv Richards’ West Indies 29 years ago.
Score Board
TOSS: ENGLAND
ENGLAND FIRST INNINGS 302
AUSTRALIA FIRST INNINGS 328
England second innings (33-2 overnight)
Cook c Starc b Hazlewood 7
Stoneman c Smith b Lyon 27
Vince c Smith b Hazlewood 2
Root lbw b Hazlewood 51
Malan c Smith b Lyon 4
Ali st Paine b Lyon 40
Bairstow c Handscomb b Starc 42
Woakes c Smith b Starc 17
Broad c Paine b Starc 2
Ball c Handscomb b Cummins 1
Anderson not out 0
Extras (NB-2) 2
Total (all out; 71.4 overs) 195
Fall of wickets: 1-11, 2-17, 3-62, 4-74, 5-113, 6-155, 7-185, 8-194, 9-195, 10-195.
BOWLING: Starc 16-1-51-3 (1nb), Hazlewood 16-3-46-3, Cummins 12.4-4-23-1, Lyon 24-4-67-3 (1nb), Smith 3-0-8-0.
AUSTRALIA SECOND INNINGS
Warner not out 60
Bancroft not out 51
Extras (LB-2, NB-1) 3
Total (0 wkt; 34 overs) 114
BOWLING: Anderson 8-2-17-0 (1nb), Broad 7-2-14-0, Ali 4-0-23-0, Woakes 7-1-31-0, Ball 4-1-17-0, Root 4-1-10-0.
Match officials: Umpires: Aleem Dar (PAK), Marais Erasmus (RSA); TV umpire: Chris Gaffaney (NZL); Match referee: Richie Richardson (WIS).