Former world No.1 Day is in contention, at four under par, to add a green jacket to the PGA Championship title he won 10 years ago, sitting four shots behind English leader Justin Rose entering the weekend.
A bogey on the 18th on Friday was Day's first for the tournament in a demonstration of mistake-free golf not seen at Augusta National Golf Club since Ed Sneed went 36 holes without a blemish in 1979.
Min Woo Lee (one under) was the only other Australia to make the cut, after Cameron Smith, Adam Scott and Cam Davis all struggled.
The pair will continue low-profile assaults on the year's first major on Saturday (Sunday morning AEST), with all eyes on Northern Irishman Rory McIlroy (six under) and his quest for a career grand slam.
Big-hitting US LIV Golf star Bryson DeChambeau (seven under), who has crushed 874 range balls this week, will be in the final group with Rose.
Americans have won the last seven major titles, defending champion and world No.1 Scottie Scheffler and compatriot Matt McCarty (both five under) the only others in the top 10.
Canada's Corey Conners, Ireland's Shane Lowry, Brit Tyrrell Hatton, Dane Rasmus Hojgaard, Norway's Viktor Hovland, South Korean Sungjae Kim, Swede Ludvig Aberg and Japan's former champion Hideki Matsuyama are all in the top 12, within five shots of the lead.
"I'm kind of under the radar, which is nice ... sitting at a tie for ninth is good going into the weekend," Day said.
"I just keep my head down and keep pushing."
Day is back with Swatton, who spent two decades in his corner as a swing coach and caddie before calling time in 2020.
"It was definitely me," Day said of how he prompted their reunion.
"I was doing my own thing, kind of, at the end of the year. As a professional golfer, you can't. You need a good solid team around you.
"We text these days ... I sent swings through and said, 'Hey, can you look at this', and then that kind of evolved into more texts and more calls."
Day admits he thinks "all the time" about 2013, when he lost a late Sunday lead that allowed compatriot Adam Scott to instead swoop and become the country's first Masters champion.
That's why he and Swatton will keep things steady and simple this weekend.
"It's nice to have somebody come in and make things a little bit more clear, as in not as complicated as I was making it," Day said.
"He just said, 'You've got to fly the plane. Just go out there and fly the plane'.
"Some weeks you're not going to have the best stuff, so just go out there and try and get it done."
McIlroy, chasing his first major since 2011, made two late double bogeys on Thursday to drop to even par before staging an emphatic recovery on Friday.
But he, like Day, knows how tough it can be with the finish line in sight after shooting a fourth-round 80 to cough up a four-shot lead in 2011.
"Just get yourself into contention on the back side," Day said of what he's learnt in 14 tournament starts.
"Anything happens on the back side ... there's proof of certain people that have struggled on the back side and certain guys that have played well on the back side and won.
"I know it's going to be tough (on Saturday), but get the opportunities, try and capitalise on them and then get myself into contention on the back nine on Sunday."
AUSTRALIANS IN MASTERS THIRD-ROUND ACTION
* Min Woo Lee (one under) - 12.30pm (2.30am Sunday AEST)
* Jason Day (four under) - 1.50pm (3.50am AEST)
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