The fourth and final Test is in Sydney.
Khawaja 101*, Green 74, and Leach 4-84) were the decs.
Crawley was the top scorer with 77 points for England .
Australia leads the series by three games.
The scorecard is a summary of what happened.
Australia's hopes of a clean sweep in the series were ended by a tense draw on the final day of the fourth Test.
The tourists were 13 balls from safety when Steve Smith was hit by Jack Leach, leaving it to Stuart Broad and James Anderson to lead England home.
With the light fading and every Australia fielder around the bat, Broad and Anderson blocked out Smith and Lyon to secure a hard-fought draw.
Ben Stokes hit 60 despite still struggling with his side injury as England crept towards safety.
Pat Cummins took two of the three England wickets in three balls to rattle the tourists.
England's players were barely able to watch as Anderson played out the final over in a thrilling end to the match.
Australia lost seven overs as they tried to force victory on Sunday, with rain meaning they lost on the fourth day.
The final Test of the series will be played in Hobart on 14 January.
England battle through the final hour.
England showed real fight and character during the match, even though they had already lost the Ashes.
Bairstow showed his strength with his first-innings century and the tourists fought hard to repel Australia on the final day.
The small crowd at the Cricket Ground in Australia was at their loudest in the final hour as Australia tore in with the new ball.
Cummins, who had been subdued with the ball throughout the day, trapped Buttler LBW on review before bowling Mark Wood two balls later with a delivery that knocked the bowler off his feet.
Bairstow was nursing a thumb injury that may keep him out of the next Test, so he was the one who had to see off 15 overs.
Bairstow popped a catch to short leg when Smith dropped him, but Australia would have felt victory was in their grasp.
The players chirped around the bat as Broad and Leach stood their ground, but Smith was disappointed when he was dismissed by a short, fast, hostile bowling.
Broad and Anderson were left to give England something to smile about after a difficult tour.
The man stands tall.
In the morning session, Crawley's performance showed what could be in the future.
The bowlers were not allowed to settle by Crawley, who started strongly the previous night. He pulled and drove the off-colour Starc before flicking Lyon away to bring up a 69-ball half-century.
Bairstow and Stokes did the same thing on the third day, throwing Australia off their plans.
He had scored 77 by the time he fell. The three England batters had scored 19 runs.
The two men shared a 43-run stand. This was England's third highest opening partnership in the last four years, and shows how long their Test batting has been falling away.
The Crawley was showing a lot of energy at the other end.
He was dropped by Alex Carey off Cummins but was able to register his sixth consecutive single-figure score. He is unlikely to play in the final Test.
After battling so bravely that he almost punched his bat as he sent a simple catch off Lyon to Smith at slip, Joe Root was left aghast as he nicked behind and the other two were also caught by Smith.
The draw in Australia will raise England's spirits, but they will know that their batting problems are still there, and that they have still to pass 300 on this tour.
They said that weather forecasts are useless.
"Relief is the overwhelming emotion and I'm quite proud too," said England captain Joe Root. The guys have stood up and shown a lot of character and pride, even though we had a lot thrown at us.
Today shows how much it means to them. It is important that you show how much it means to you when you are out of the series. I think everyone has done that this week.
Pat Cummins said that the game was a great one. We were close. The weather forecasts are useless. This week, I learned that.
I thought we had left ourselves enough time. Today was fun.
It could have gone either way, says the player of the match. We couldn't have asked for more.
I'm enjoying the game. I like it. There are ups and downs. I could get two ducks the next time I play.
It was only a draw, but for the players and fans, it means a lot.