While Woods completed his comeback round with a dreaded shank at the last hole, Day and fellow Australian Cam Davis had no such trouble in opening with six-under-par 65s to share second spot at Riviera Country Club.
Day was particularly impressive, chalking up six birdies in a bogey-free round after starting with six straight pars at the $US20 million ($A31 million) Signature PGA Tour event.
"It's really nice," he said after going six under for his last 12 holes.
"I didn't get myself too far out of position. When I was, or in the rough, I was able to get myself back into the green, make my par and move on."
The near-flawless display was a far cry from 17 months ago, when a debilitating back injury sent the former world No.1 spiralling to 175th in the rankings.
"There were times where I wouldn't really practise Monday, wouldn't really practise Tuesday, just try and get through the pro-am and go, 'OK, if I can get through Thursday and Friday, then great'," Day said.
"To be able to get that back in the rear-view mirror now, where I can focus on actually practising and putting good work in, it's been nice because for a moment there I just didn't know if it was really going to pan out for me.
"I thought maybe I'm at the end of it in regards to my playing days."
Back up to world No.19 after ending a five-season title drought last year and finishing joint runner-up at the British Open, Day says he would have regretted not trying to return to the top of golf.
"It would have been thoroughly disappointing to sit there and go, 'Oh, man', like I felt like I've got more gas in the tank," he said.
"That's why I didn't quit on my body, it just took some time. It's nice to be able to see light at the end of the tunnel."
Davis racked up seven birdies after making bogey at the par-4 second to also sit one shot behind American first-round leader Patrick Cantlay.
"Honestly, I didn't hit the ball super-great today," Davis said.
"I had a couple of wayward ones, but I missed it in places that were not too bad to get up and down from.
"It was a weird round, I really built it slowly. I was surprised how many birdies I made on the back nine."
Cantlay was eight under through 14 holes before recording his only bogey on the par-3 16th to sign for a 64.
His countryman Luke List is tied for second alongside Day and Davis, with fellow Americans Jordan Spieth, Tom Hoge and Will Zalatoris one stroke further back at five under and in joint fifth.
Playing his first official tournament since last year's Masters 10 months ago, Woods carded a one-over 72 to be tied for 49th in the elite 70-man field.
The 15-time major winner mixed five birdies with six bogeys, including at the 18th after he shanked his approach from the fairway.
Playing on a sponsor's invite and in the final group of the day, Australia's two-time champion Adam Scott also posted a 72.
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