Labuschagne also emerged as the leading run-getter in the three-match rubber, amassing 275 runs from four innings with an impressive average of 68.75.
Warner didn't look impressed with the decision and argued with Dar and square leg umpire Marais Erasmus over the incident.
Australia registered an emphatic 279-run victory in the third and final Test against New Zealand to complete a 3-0 whitewash.
Lyon was the standout bowler, making the most of the slow and variable bounce in the pitch to return 5-68, his best figures in nine tests at his home ground and 17th five-wicket haul of his 96-test career.
Labuschagne scored 215 off 363 balls, with 19 boundaries and a six, before his epic innings was ended amidst a late order collapse by the hosts to be all out for 454 by tea on Saturday.
The world’s fourth-ranked batsman has scored 837 runs in five matches, including four centuries, this summer at an incredible average of 119.6.
Labuschagne took 346 balls to breach the 200-run mark in which he slammed 19 fours and a six.
Lanuschange, who only a few months back was called up as a concussion substitute for Smith, has once again scored a century, the first for this decade, en route to his unbeaten 130 on day 1 of the third Test against New Zealand
Marnus Labuschagne shared a 156-run partnership with Steve Smith, who made 63, to give first-day honours to Australia after captain Tim Paine won the toss and batted on a dry SCG pitch.
As soon as the 30-year-old scored his first run, the SCG burst into ironic cheers and even the Australian batter could see the funny side, raising his arm to acknowledge the applause.
Skipper Williamson and Nicholls were too unwell to train on Wednesday and Thursday, while spinner Mitchell Santner - who was facing the axe regardless, after an ineffectual start to the series - has also fallen ill.
With many parts of the country in the grip of devastating fires, the third Test between Australia and New Zealand at the SCG starting on Friday will be played amid smoke from the nation's unfolding bushfire crisis.
Black armbands will be worn from the first day of the Test on Friday as a mark of respect for those who have lost their lives in the tragic fires.
Air quality has been a regular concern for Sydney residents in recent weeks and the smoke is expected to be at its worst on Saturday.
Australia head coach Justin Langer has said that a change is unlikely in the playing XI for the third and final Test against New Zealand.
Since debuting against Pakistan in Abu Dhabi one year ago, Somerville played two further Tests for the Black Caps in Sri Lanka in August and boasts 14 wickets at an average of 25.
Despite a heavy defeat and a subsequent series loss in Australia, Williamson remained gracious as always
Cummins' 99 wickets came in 35 matches at 20.50 an average and strike rate of 36.8 with three fi-fers and one ten-wicket haul. He also finished as leading wicket-taker in Tests in 2019.
Williamson’s dismissal for a duck helped trigger a top-order collapse as New Zealand lost three wickets for three runs to be 35-3, before being bowled out for 240 and crashing to a 247-run loss at the Melbourne Cricket Ground.
Australia hammered New Zealand by 247 runs in the second Test at the historic Melbourne Cricket Ground (MCG) on Sunday.
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