The Australian shot 32 on the back nine to post a six-under 65 at Monterey Peninsula Country Club, one of three courses in use for the first three days of the tournament.
Baddeley was one under that included two birdies and a bogey on the front nine before finishing with a blistering run home to be tied fifth, along with Frenchman Martin Trainer and American Eric Cole.
He began with eagle on the par-five 10th before adding birdies on the 13th, 14th and 15th to come within two of outright leader Hank Lebioda, who piled up nine birdies for his 8-under 63.
Lebioda went 5 under on the back nine, while Kurt Kitayama and England's Harry Hall shot 7-under 64s to share second with Chad Ramey, who posted a 7-under 65 at Pebble Beach Golf Links.
All players will play one round apiece at Pebble Beach, Monterey Peninsula and Spyglass Hill Golf Course before a 54-hole cut. The low 60 players and ties will play Pebble Beach in Sunday's final round.
Lebioda, 29, has yet to win a PGA Tour event and missed the cut in his first five starts of the 2022-23 season. His 63 tied a career low on tour.
"For probably the last couple weeks or so I felt like my putting had really turned a corner, even though I may not have shown the results," Lebioda said.
"But I felt more confident standing over the ball. I liked what I was looking at visually standing over it. I knew it was just a matter of time. So today fortunately it was one of the days where quite a few of them did go in."
Lebioda said his game plan for now is simply to have fun.
"If it's blowing as it is right now it will be definitely a tough challenge playing Pebble Beach tomorrow," he said after the Thursday round.
"But I'm going to rest tonight, get my body ready and try to go out and do more of the same."
Kitayama was bogey-free, while Hall eagled the par-5 16th and had a five-birdie run at Nos. 3-7.
Spyglass Hill is considered the most difficult of the three courses. The low round of the day at Spyglass Hill was Keith Mitchell's 5-under 67. Mitchell had six birdies and just one bogey.
Notable names include Englishmen Luke Donald (4-under 68 at Pebble Beach) and Justin Rose (3-under 69 at Pebble Beach), Viktor Hovland of Norway (2-under 70 at Spyglass Hill), 2017 champion Jordan Spieth (1-under 71 at Spyglass), defending champion Tom Hoge (1-under 71 at Pebble) and US Open champ Matt Fitzpatrick of England (1-under 71 at Spyglass).
Australian Greg Chalmers shot a four-under 67 at Monterey to be tied 13th, while compatriot Geoff Ogilvy is two further behind after his 70 at Pebble Beach.
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