The pair sit at 20 under and hold a two-stroke lead over first-round leaders Tony Finau and Nelly Korda, who struggled to a 70 on Saturday.
Lucas Glover and Leona Maguire are tied for second at 18 under after carding a 69.
There's a four-way tie for fourth at 16 under.
The tournament features 16 mixed teams with one male and one female player.
Saturday's format was foursomes, with each team's players hitting alternate shots with the same ball until the ball is holed.
Australia's Day and New Zealander Ko - both former world No.1s - offset their lone bogey with seven birdies to vault into the lead.
"This is just a great experience for me," Ko said of the tournament's mixed gender pairs format.
"I hope a lot of juniors ... get inspired and hope that one day they play on the PGA or the LPGA and they too are paired up with a fellow player (from) the other tour," Ko said.
"This is the outcome and the result is secondary.
"We don't really get to cross paths that much with other tours. Jason's only the fourth PGA Tour player I've played with.
"It's great, something that I can learn a lot from."
Rickie Fowler and Lexi Thompson were the only team with an eagle in the second round, with 11-time LPGA Tour winner Thompson recording an ace at the par-three 16th.
17°C