Davis closed with the equal low round of the tournament, a daring five-under-par 65, to share fourth spot at three under with Americans Kurt Kitayama and Bryson DeChambeau.
He briefly held the clubhouse lead before finishing six shots behind US winner Brooks Koepka.
The top-four result earned the 2017 Australian Open champion a return to Augusta National next April after Davis tied for 46th in his only previous Masters appearance last year.
Now the 28-year-old Australian hopes to build on easily his finish at a major, with his next chance coming at the US Open in Los Angeles.
"Every time you have a really good round under tough conditions, it's just another little positive voice in the back of your head that, yeah, I can do this even when it's difficult," Davis said.
"Even when the rough is really deep and the pins are tight and firming up quick, you can still play really good golf and make a score especially toward the end of a major.
"That's where I want to be. I'd love to win one or more of these for sure.
"This is just one more step towards that goal."
Not holding back in pursuit of third-round leader and ultimate champion Koepka, Davis shared the clubhouse lead for more than an hour after racking up an eagle and four birdies on Sunday.
The highlight was driving the green on the 320-yard par-4 14th and draining the eight-foot eagle putt to the roars of the crowd.
"It was awesome," Davis said.
"I was pretty pumped up, but at the same time you have to to go to the next hole and calm yourself down and hit a finesse shot. It's a pretty unique up-and-down of emotions.
"But I hit a lot of good ones. Feeling really pumped up today, which is great."
Countryman Cameron Smith, the reigning British Open champion, also took advantage of the perfect scoring conditions with a 65 to finish ninth, his first PGA Championship top 10.
In another glimpse of what the PGA Tour has been missing since his defection to LIV Golf, Smith collected seven birdies and made a clutch 14-foot par putt at the last to ensure the world No.8 finished in red numbers at one under.
"The goal today was to get back in the red and just kind of see what happens," Smith said.
"Obviously, the course softened up yesterday with all that rain, and the fairways were holding up a little bit more rather than running off into the rough.
"The greens were quite receptive, too. It was definitely a gettable golf course.
"Yeah, just happy to really just string a round here. That was good to see."
After starting his round as the leading Australian, Min Woo Lee's final-round 71 left him at two over and equal 18th.
Adam Scott closed with a 69 to finish his 87th consecutive major championship at five over par, one shot better than Lucas Herbert, who had a final round of 70.
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