World No 2 Rory McIlroy fell seven shots behind the leader after suffering three consecutive bogeys and a double-bogey on the back nine.
"The back nine was a bit of a battle," McIlroy said.
"I think [the afternoon starters] will feel like they got the rough end of the draw [with the conditions], but still feel like I'm in the tournament and in with a decent chance."
McIlroy remains tied at even par alongside world No 1 Scottie Scheffler, who posted a resilient 68.
"If there's a course where you feel like you still have a chance if you're seven back going into the weekend like I am, it's definitely this one," McIlroy said.
Further down the leaderboard, Dustin Johnson dropped out of contention following a quadruple-bogey on the 15th hole.
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Former champions Bryson DeChambeau and JJ Spaun both missed the four-over-par cut line, while Joaquin Niemann made history by qualifying for the weekend despite recording an 11 on a single hole during his opening round.
