Fellow Australian Min Woo Lee is also in the mix for the Wanamaker Trophy but 2015 champion Jason Day's hopes of winning for a second time perished during the third round in Pennsylvania.
Smith and Lee will start the final round just four shots behind surprise leader Alex Smalley after producing starkly contrasting rounds at Aronimink Golf Club on Saturday.
After missing the cut at the past six majors, Smith surged with a two-under-par 68, while Lee ground out a steely 71 featuring three bogeys and a dreaded double.
Smith, the 2022 British Open champion and one-time world No.2, last week revealed his gut-wrenching decision to part ways with lifelong coach Grant Field.
Field had been in Smith's corner since he was a Brisbane junior but, after missing the cut again at last month's Masters, the 32-year-old turned to Claude Harmon III, the son of swing guru Butch Harmon.
"It was a terrible, terrible conversation to have," Smith told todaysgolfer.com of the decision to split with Field.
"I've been seeing Grant since I was like nine years old, and he's a really good friend as well, so it was tough."
But the change-up has paid immediate dividends this week in Philadelphia.
Golf's sleeping giant only found six fairways on Saturday but, as he does, the short-game wizard scrambled brilliantly and only needed 28 putts for the round.
Smith enjoyed a spectacular mid-round burst of four birdies in five holes either side of the turn but cursed himself for lipping out from seven foot with the chance to pull to within one stroke of the lead on the par-3 14th.
Smith, though, held his cool to par his last four holes to give himself a winning shot on championship Sunday.
Lee fought desperately to also stay in contention with a rollercoaster third round.
He offset back-to-back bogeys on holes three and four with successive birdies on six and seven, where he drove the green at the 397-yard par 4.
But just as he moved back to within a shot of the lead, Lee made a complete mess of the par-5 ninth.
Going from rough to rough and then three-putting, he racked up a disastrous double-bogey seven on a hole playing the second easiest of the week.
Deflated, Lee missed a short birdie putt on the next hole, then dropped another shot on 13 before making birdies on 14 and 18 to clamour back into red figures and a tie for 11th with Smith.
From a position of promise, Day misfired to lose all hope.
Like Lee, he rebounded from two early bogeys with consecutive birdies only to also post a dreaded double on the treacherous 10th hole to slip from one under to over par.
Playing catch-up, Day dropped three more shots in his last four holes for a 75 to wind up at four over - a distant 11 strokes adrift of the pacesetter.
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