But the Thai mixed in six birdies over an 11-hole stretch and it added up to a 67, leaving her two shots back and tied for second along with Lydia Ko (68) and Ji Eun-Hee (67).
Mickelson's 16-under total of 128 put him two strokes in front of Australian rookie Curtis Luck, who grabbed his eighth birdie of the day at his final hole - the ninth - to post a 66 on the Nicklaus course and a 14-under par total of 130.
"I really didn't think that this was going to be a day that I was going to go low", said Mickelson, who tweeted prior to his round that he was "a bit rusty, but also fresh and ready to get started".
PGA West's Stadium Course in La Quinta, California is the host course for the 60th anniversary of the Desert Classic.
Mickelson said he would have to stay aggressive on the weekend.
"Sometimes you have days where it just clicks".
After the turn, Mickelson tallied five birdies in his next seven holes. He got back to under par with a birdie on fourth and then had three in a row from seventh to ninth.
He closed with another birdie on the par-four 18 to record the 37th all-time round of 60 on the Tour.
But his approach shot on 17, with a sand wedge, left him with a longer putt than he had hoped for.
Asked to compare his second round with his 60, the American said: "I actually felt better striking it but I didn't putt very well relative to yesterday where I was making everything". "I kind of eased into it, thinking that if I hit it too hard it might hit the pin and miss".
"I feel uncomfortable right now because I don't know them well enough and I've been trying to get a seminar to learn them all, and I just haven't had time or a chance to", he said.
"That was an interesting shot because I could have easily lost one and I ended up picking one up", he said.
The tournament victor in 2002 and 2004, Lefty will play the final two rounds on PGA West's Stadium Course.
Top-ranked Justin Rose was tied for 28th at 8 under after a 68 on the Nicklaus layout.
"I drove the ball fantastically well today and hit a lot of shots pin high with my irons".
Jon Rahm, the 2018 Desert Classic champion, is now in a three-way tie for fifth place (12 under).
Power is at three-over par with well adrift of the projected cut which will see the top 70 players - the Waterford native is tied for 151th in the field - advance.