Rory McIlroy had no form on the fast putting surfaces as he signed for a 74, which included three bogeys and a double-bogey having taken five shots to get down from 112 yards out at the par-four 13th.
The Northern Irishman's chances of getting back into contention look slim as he is 10 strokes behind Poston, as is Scottie Scheffler after a level-par 72.
Poston's seven-under round of 65 was four shots better than any other player in the field at Muirfield Village in Ohio on Friday (Saturday AEST) and leaves him nine under the card.
"I just knew it was going to play tough and the goal was to try and be patient and keep hitting the shots like I was hitting yesterday and it helps to get off to a great start, make a few nice, longish putts the first couple holes and I feel like I was just kind of off and running," he said.
First-round joint leader Tommy Fleetwood went backwards with a 73 to drop to fourth, five off the lead.
"It was pretty brutal, actually. I still think I got a good score out of that today," he said.
"I made a bogey on one and six, where I didn't really feel like I had done anything wrong whatsoever."
Scheffler's bid to win for a third successive year remains alive thanks to three birdies in his last six holes, having recorded three successive bogeys from the eighth and escaped with a par after a shank out of a bunker at the fifth.
"Overall it was a tough day, I felt I could have shot 90. I may be a lot of things but I'm not a quitter," the world No.1 said.
"That's maybe some of the worst I've hit it in a couple years out there and I still managed to shoot even par around a golf course that requires you to strike the ball really well."
US PGA champion Aaron Rai (70) and fellow Englishman Alex Fitzpatrick (71) are in a share of ninth at one under, alongside Ireland's Shane Lowry (73).
Adam Scott (74) was the only Australian to make the cut at two over, while compatriots Jason Day (76) and Min Woo Lee (78) finished six and eight over, respectively.
With the AP & AAP.
