Labuschagne made 103 and Smith scored 93 before Australia's tailenders knocked off some quick runs against England's worn-out bowlers and Australia declared after tea.
Lyon joined legspinner Shane Warne, who took 708 test wickets between 1992 and 2007, and paceman Glenn McGrath, who took 563 between 93-'07, as the only Australians to surpass the 400-wicket barrier in test cricket.
Match Referee David Boon imposed the sanction after Joe Root's side was found to be five overs short of the target with time allowances taken into consideration.
Australia set a target of 20 runs for victory, finished the job in the sixth over for the loss of Alex Carey.
Australia clinched a strong nine-wicket victory over the Joe Root-led England on Day 4 to take a 1-0 lead in the five-match Ashes series.
Cummins' first match as the Test captain of Australia was a memorable one, picking his first five-wicket haul against England.
Ashes 2021-22, AUS vs ENG 2021, 1st Ashes Test, Day 4 Live Score: Follow live commentary, all live updates and scores from ongoing Australia vs England opening Test at the Gabba, Brisbane.
Stokes had dived to stop a ball racing to the boundary in the first session. He appeared to get up sore and barely bowled after the incident.
On-field umpires did not get help from the technology that helps check the front foot on every delivery. It was reported that the equipment that does this had broken down and Stokes went on to bowl a total of 14 no-balls, with only one getting detected.
The Ashes 2021-22: Catch Day 3 Live Cricket Score, Latest Scorecard, Commentary and the Latest Updates as Australia take on England in the first Ashes Test at The Gabba in Brisbane.
England beat Australia by eight wickets in their Super 12 Group 1 match of the T20 World Cup.
Title favourites England are expected to be tested for the first time in the ongoing T20 World Cup when they face arch-rivals Australia in a battle for supremacy in the Super 12 Group 1.
Khawaja had picked up a hamstring injury during Australia's clash against South Africa in the recently concluded World Cup and was subsequently ruled out of the tournament.
Injury-hit Australia could see some new faces play in the WC semifinals against arch-rivals ENG but coach Justin Langer is optimistic of the reinforcements filling in the void
Melbourne: Brad Haddin brought up a defiant half century before Australia was dismissed for 204 on Saturday, trailing England by 51 runs on the third morning of the fourth Ashes test.Haddin and Nathan Lyon added
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