A long birdie putt on the 18th helped Smith to a one-under-par 71 on Thursday, despite the 2022 British Open champ hitting just six greens in regulation and finding eight of 14 fairways on Thursday.
Things went similarly for Smith a year earlier, the 31-year-old battling on to finish in a tie for sixth, his fifth top-10 finish in the last seven years.
Akshay Bhatia's birdie blitz on the back nine saw him join Day at two-under and push Smith and compatriot Min Woo Lee (71) to equal 11th.
Only the great Tiger Woods, in 2005 and 2019, has won the tournament from outside the top 10 after the first round in the last 20 years.
But, with winds expected to pick up, Smith has found some confidence with the flat stick.
"Putting seems unreal at the moment," he said.
"This whole start of the year I've hit a lot of good putts and even a lot of great shots and haven't really got much out of it.
"Today I definitely got the most out of my round, which is a good way to start.
"It gives you the confidence to go at some pins and do stuff you wouldn't normally do and be aggressive. Looking forward to the weekend."
Compatriot Day, who was blemish free in his breezy round, warned against that approach though and admits it's always tough to claw back ground at the year's first major.
"I just struggle to think that anyone can shoot a low one, although it has been done," he said.
"It's very, very easy to kind of push and start being aggressive, and you cannot do that around here.
"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."
LIV Golf talent Smith, seeking his first title in nearly two years, needed to draw on some early magic, threading a narrow gap after pulling his drive off the first tee.
His iron snuck between two huge pines and curled back towards the green, Smith then two-putting for par.
"I don't think there was too many choices out there, to be honest," he laughed.
"They were all kind of a bit crappy. I've been in there a lot actually, on that left side, so I felt right at home."
He then scrambled with a long bogey putt on the fifth to avoid serious damage and drained a longer birdie putt from the fringe of the par-three sixth to return to even par.
That's where he stayed for the next 11 holes until a walk-off birdie at the 18th kept him in the conversation.
"I haven't left myself too much work," he said.
"For how I felt out there, it felt like it was going to be a bit of a long day.
"If I'm going to win this thing, I definitely need to do better than that but golf is such a weird game."
