Fowler had three par putts of 10 feet or more. He has gone 45 straight holes without a bogey at Bethpage Black.
Along with having a chance to win his first PGA Tour event in a year, Fowler is in prime position to earn a spot on the U.S. Ryder Cup team.
He was at 9-under 204.
Reed overcame a stretch of bogeys early for a 71, missing birdie chances on the last two holes.
Adam Scott had a 65, the low score of the tournament, and was two shots back.