Rosie Jones posted the round of the day at 5-under 67. She climbed into a share of third place at 1-under-par 143. Jones was joined there by Cristie Kerr (69) and Se Ri Pak (70). Defending champion Annika Sorenstam shot a second-round 70 to move into a share of sixth with Lorie Kane (74) and Michele Redman (72) at even-par 144.
Davies finished her opening round at 1 over par after posting a 4-over 40 on the back nine at Trump International Golf Club. Friday, she bogeyed three of her first six holes to fall to plus-4.
The Englishwoman turned the switch from there and exploded up the leaderboard. She birdied No. 7 from 12 feet out to begin a stretch of three straight birdies that helped her climb back to 1 over.
Around the turn, Davies birdied the 10th for her fourth consecutive birdie. She then drained back-to-back birdies from the 12th to move to minus-2 and tie Mallon for the lead.
Davies, who had been six strokes behind Mallon through six holes, stumbled to a bogey at the 14th when she missed the green, falling a shot behind Mallon.
Davies came right back at the par-5 15th with a two-putt birdie to rejoin the lead. She parred in to remain tied atop the leaderboard.
'It was very different day than Thursday, a very up-and-down day,' said Davies. 'This golf course, I keep saying, you can play identical shots and walk off with a birdie one day and a hit a similar shot on another day and end up with a bogey. It's a hard test of golf.'
Mallon, who trailed by two strokes entering the round, jumped out of the gate with a 25-foot birdie at the second to move to minus-2. The rest of her front nine was a roller coaster, though.
The 14-time winner on the LPGA bogeyed the fifth after missing the green, but responded with a five-foot birdie at the very next hole.
Mallon faltered to another bogey at the seventh when she was unable to get up- and-down, but again rebounded quickly. She rolled in a birdie on the eighth to move back to 2 under.
Around the turn, Mallon three-putted for a bogey on No. 10, then birdied the 11th after dropping a 6-iron within a foot of the cup to erase the mistake. She rolled off six straight pars to head to the last tied for the lead.
On No. 18, Mallon's tee shot barely cleared the water and ended in the right rough. She managed to hack her shot out and knocked it pin-high, but in the greenside rough. She chipped her third shot that lipped out before tapping-in for par to remain tied for the lead.
'I actually felt like I hit the ball a little bit better today,' Mallon said. 'Actually my touch was a lot better today except for that three-putt that I had on No. 10.
'I am playing too good to make the little mistakes, the three-putts, and missing the three-, four- and five-footers that you need to make to win.'
Overnight leader Laura Diaz struggled to a 5-over 77 on Friday. She fell to 2-over-par 146 and is tied there in ninth place by Becky Morgan. Beth Daniel and Patricia Meunier-Lebouc are tied one stroke further back at plus-3.
Hee-Won Han and Karrie Webb are tied at 4-over-par 148, while Mi Hyun Kim and Angela Stanford are at plus-5.