The second Test is in Adelaide.
Australia 473-9 dec (Labuschange 103, Warner 95, Smith 93)
England 236 and 192.
Australia won by a wide margin.
The scorecard is a summary of what happened.
Australia took a 2-0 lead in the series after defeating England in the second Test in Adelaide.
Needing to bat out the day for a draw, England went into the final session with the expectation of taking the game into the final session.
The slim hopes of the most unlikely of England escapes were dashed when Buttler fell in the second over of the night session.
He saw off 31.2 overs with Chris Woakes, who made 44, and another 14.2 with Ollie Robinson, but stood on his stumps when going back to a shorter ball from Jhye Richardson.
James Anderson was the last man to be caught by Richardson. England were 192 all out.
It leaves their hopes of a first series win in Australia since 2010-11 fading as the tour moves to Melbourne for the third Test, which begins at 23:30GMT on 25 December.
England have never come back from 2-0 down to win the series.
The England fight was too late.
The result was still an emphatic Australian victory despite England's final-day exploits.
Buttler had hidden his attacking instincts which made him one of the best limited-overs players in the world.
There were fears that England could go within a session after Ollie Pope was caught at slip off Mitchell Starc for four in the second full over of the day.
Their fate was sealed on the third day when they served up their latest batting collapse.
It was expected that England would lose their 11th in the past 12 Tests in Australia.
The day-night Test was seen as helpful to England's cause, the floodlight conditions and pink ball were supposed to help their seam and swing bowlers, and Australia were without captain Pat Cummins and Josh Hazlewood.
Only once has a team come from 2-0 down to win the series, and that was with Don Bradman in 1936-37.
The next Test is at the famous Melbourne Cricket Ground, the one venue England have avoided defeat in their winless run down under.
Buttler shows the way.
Alex Carey let the ball fly between him and David Warner when Buttler nicked Starc early on, but he was lucky not to make his second duck of the match.
Buttler's place in the third Test is likely to be secure until he plays a back-foot push on the off stump.
Buttler's most able partner throughout the day was Woakes. He survived 97 balls but 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611
Pope needed to secure his place but only lasted seven balls.
He poked at a ball he could have left from Starc on four, but Ben Stokes missed a straight ball on the back foot and fell for 12 from 77 balls.
More to come.
