The Australian began the second round at the Riviera Country Club in 77th position after carding a one-over 72, but on Friday he rocketed to joint 21st with a four-under 67.
Day is now three under for the tournament, seven behind leader Max Homa (68).
The 35-year-old is enjoying a fine vein in form in 2023 after a horror spate of injuries resulted in him plummeting down the world rankings.
He began his renaissance with an 18th-placed finish at the American Express before tying for seventh at the Farmers Insurance Open. It was followed by an impressive fifth at the Phoenix Open.
On a day when players found scoring difficult, the Queenslander's 67 was behind only second-placed American Lee Hodges' 66.
He was faultless all day, making birdies on the sixth and ninth and adding two more on the back nine to be nicely poised for the weekend.
Compatriot Lucas Herbert, who had a one-under 70 on Thursday, pieced together another solid round to rise 12 places.
The 27-year-old from Bendigo added an even-par 71 to be tied 33rd in a large group comprising two-time PGA Championship winner and former world No.1 Justin Thomas and Tony Finau.
After his promising 69, Adam Scott had a two-over 73 in the second round to be level for the tournament.
Scott is tied 51st but he flirted with the one-over cut with a 39 on the back nine, which included a double-bogey sandwiched between two others.
The former world No.1, who was elected chairman of the PGA Tour's players' council earlier this week, steadied the ship, however, with birdie at the last.
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