Marsh, who was playing his first test since December last year, had a brilliant spell of 3-16 in seven overs after tea and is likely to finish with the best bowling figures of his career in tests. The only other time he took four wickets in an innings was when he had 4-61 against West Indies in Melbourne in 2015.
"I had a fair bit of adrenalin running through my body and I probably haven't bowled a spell that long," said Marsh, who had to cut short his 17th over of the day after just one ball because of cramp.
"I was like a kid at Christmas this morning. It can be a long tour when you are not playing. I just wanted to try and get an opportunity at some stage and it was nice to produce today."
From 170-3, England lost five wickets for 56 runs only for Buttler to launch his fightback. Hit on the chest on 17, he decided to take matters into his own hands and peppered the boundary — unloading three sixes and six fours in his 84-ball knock.
"With the new ball not being far away, I thought it was the best time to go for it and I was just trying to have some fun, too," Buttler said.
"Batting has been hard work and not enjoyable this series so I wanted to take the shackles off and play with a smile on my face."
Paine was influenced by what he described as a "strange-looking" pitch with a tinge of grass.
Rory Burns and Joe Denly managed to scramble together 27 runs in just under 10 overs — remarkably the highest opening stand of the series — before Pat Cummins parted them, Denly (14) with a familiar waft outside off stump and Steve Smith taking the slip catch after a couple of fumbles.
Any doubts Paine had over his decision at the toss would only have intensified when Root top-edged a pull from Cummins only for Peter Siddle to let the ball slip through his hands at fine leg.
Root was spared again moments later when Cummins took his outside edge but Paine put down the chance, having leapt one-handed in front of David Warner at first slip. Burns took the opportunity to settle things down, guiding the score to 86-1 at lunch.
Australia's profligacy in the field continued in the first over of the afternoon session, Siddle this time the victim rather than the perpetrator. He tempted Root into flashing away from his body, only for Smith to parry a simple chance in the cordon.
Unlike Root, Burns didn't get to his half-century, trying to do too much with a well-directed short ball from Josh Hazlewood on 47 and looping the easiest possible catch to Marsh as he strolled in from mid-on.
- AP