Griffin shot a seven-under 63 in the Charles Schwab Challenge at Colonial on Friday to tie Matti Schmid for the second-round lead at 11 under.
They are two strokes ahead of first-round leader John Pak and five ahead of Fowler, who made the turn in 29 before settling for a 64.
Pak, the tour rookie who opened with a 63, birdied the par-4 18th for a 68 and was a shot ahead of Chris Gotterup, a one-time tour winner like Griffin.
Gotterup was eight under after a 65. Ryo Hisatsune, a 22-year-old from Japan, was another stroke back after a 67, tied with Akshay Bhatia (66).
Scottie Scheffler, who won the PGA Championship last weekend, shot 71 and was 10 shots off the lead as the world No.1 tries to become the first player since Dustin Johnson in 2017 to win three consecutive starts.
Scheffler made the cut with a shot to spare, which extended his streak to 55, second to Xander Schauffele's 64.
A month removed from teaming with Andrew Novak to win the Zurich Classic of New Orleans, Griffin made eight birdies - seven from inside 10 feet - and saved par with a 12-foot putt from the fringe after his only bogey.
The 29-year-old has already matched his career best of five top-10 finishes from last year, including a tie for fifth at the PGA.
"I feel like I've kind of made good steps the last couple of years just kind of building to get to that first win," Griffin said.
"Now that I've got that first win, I feel like it's really freeing me up to come out and be not necessarily more aggressive, but just feel more aggressive, feel like I'm trying to win more. It's definitely been a breakthrough year, but I think there's more to come."
Young Karl Vilips moved 39 spots with his 66 on Friday. The winner of the 2025 Puerto Rico Open, Vilips had seven birdies and three bogeys and is now at four under.
The 23-year-old, who made four birdies in a row starting on the eighth, is the lone Australian in the field after Cam Davis missed the cut with rounds of 76 and 71.
Fowler has dropped to 127th in the world after being in the top 25 as recently as early 2024.
The 36-year-old followed an opening 70 with six birdies before finishing even over his final nine holes.
"It's definitely coming around," said Fowler. "Body is starting to feel better, and the game (has) been in a good spot and not very far off."
Schmid, a 27-year-old German seeking his first tour victory in his 79th start, has been bogey-free with 10 birdies over 24 holes since a double bogey on the par-4 12th in the opening round.
After his first bogey of the week on the par-4 seventh, Pak got to 10 under with birdies on three of the next four holes. Consecutive bogeys dropped him into a tie with Gotterup before Pak made a 13-footer on 18.
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