Griffin, who began the day three shots back of first-round leader Chad Ramey, carded a one-under-par 71 that brought him to six under on the week and two shots clear of Viktor Hovland, Jason Day and Will Gordon.
The only hiccup of the day for world number 78 Griffin came at the par-four 18th where he hit a wayward drive and then hit a tree with his second shot en route to a closing double-bogey.
"Yeah, it's playing tough out there. To be bogey-free through 17 holes I thought was pretty freaking good," Griffin told reporters.
"It was a grind, and unfortunately I didn't finish the way I wanted to, but the 18th hole is probably the toughest hole all day. I'm not going to be the first guy to make a double there. You're going to see a few."
Griffin reached the turn at two under after birdies at the fourth and eighth holes and then picked up another stroke at the par-four 12th where he rolled in a 51-foot birdie putt that brought him to eight-under on the week.
With playing conditions worsening the late starters, which include some big names like major winners Rory McIlroy, Scottie Scheffler and Collin Morikawa, will have plenty of work to do to post a low score.
Morikawa finished the first round one shot off the lead while Scheffler was four back and McIlroy found himself in danger of missing the cut after opening with a four-over-par 76.
World number one Jon Rahm, the pre-tournament favourite who was seeking his fourth win of the season, withdrew from the PGA Tour's flagship event due to illness ahead of his second round.
