Australian hope Smith holed a long birdie putt on the 18th to card a one-under-par 71 in Thursday's opening round, a pleasing finale to what he feared was going to be a "long day" after hitting just six greens in regulation.
In contrast, Day barely missed a target as he parred his first 11 holes before back-to-back birdies helped him finish with a two-under 70.
Lee (71) mixed grit and brilliance in his first event since winning a maiden PGA Tour title.
His birdie putt on the last lipped out as he matched Smith to finish one under.
Canada's Corey Conners was the early clubhouse leader at four under before world No.1 Scheffler drained two long birdie putts to card a bogey-free 68 and join him.
British pair Tyrrell Hatton (69) and Aaron Rai (70) were also in the top 10 while fast-starting countryman Justin Rose was six-under with five holes to play.
World No.2 Rory McIlroy birdied the ninth to move to three-under as his charge to a career grand slam - and the tantalising prospect of a Scheffler shoot-out - gathered pace.
"I'm definitely coming in under the radar," former world No.1 Day said.
"I'm not to the point of how Scottie has been playing, how Rory has been playing, some of the other guys.
"I feel very just comfortable with where my game is at right now.
"I've just got to do some work on the greens. Hopefully some more putts drop."
Lee overshot his approach to the first and dropped a shot that he immediately cancelled out on the second hole.
He was one-under at the turn and then scrambled nicely on the par-four 11th when his obstructed second shot sprayed right, narrowly missing newly-planted pines.
With the wind expected to pick up on Friday, Day had a warning of sorts for powerful protege Lee.
"It's very, very easy to kind of push and start being aggressive, and you cannot do that around here," he said.
"You've just got to just ease your way into it and just hopefully you gain some momentum.
"You can't overpower this golf course."
Lee, who battled the flu and a broken finger and still finished tied for 22nd at Augusta last year, was pleased with his efforts.
"Just lipped out," he said of his putt on the 18th.
"It's one of those things, if you're giving yourself birdie putts at Augusta National, you're doing a good job."
Cameron Davis' (74) rollercoaster round included a three-putt for double bogey and a chip in for eagle, while 2013 champion Adam Scott was four over through 10 holes.
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