Griffin's card featured one eagle and a three-birdie run at Nos.16-18 at Muirfield Village Golf Club.
He finished the day with a two-shot advantage over Collin Morikawa, a two-time runner-up at the tournament hosted by Jack Nicklaus.
Griffin, 29, won his first PGA Tour title last month at the Zurich Classic of New Orleans team event with Andrew Novak. He validated that victory with his first individual win this past week at the Charles Schwab Challenge at Colonial Country Club.
In third place was Max Homa with a four-under 68. Homa has fared better since parting with caddie Joe Greiner, who now works for Morikawa. Homa is searching for his first win on tour since January 2023.
US Ryder Cup captain Keegan Bradley and Irishman Shane Lowry are tied for fourth at three-under 69 at the $20 million signature event, which will feature a cut Friday from 72 players to the top 50 and ties, plus anyone within 10 shots of the lead.
World No.1 and defending champion Scottie Scheffler posted a two-under 70.
Only 13 players managed to shoot under par Thursday.
Australian trio Min Woo Lee (four-over 76), Cam Davis (78) and Adam Scott (79) are all battling to make the cut.Â
Others also struggling to make the weekend include Sweden's Ludvig Aberg (75), England's Matt Fitzpatrick (76) and Justin Rose (78), Wyndham Clark (78) and Justin Thomas (80).
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