Fowler also shot 68 to join a group of four players one stroke back on a leaderboard with only eight strokes separating the 90 players who made the cut.
"I'm in good position and nice to be there," Fowler told reporters. "I know I can clean some stuff up over the next couple of days."
Jordan Spieth, playing his way back into form for next week's Masters, carded 67 to trail by two strokes, while another Masters favourite Justin Rose shot 69 to lurk four back.
"From where I was three days ago, goal accomplished for the week already. From this point anything else is icing on the cake," Spieth said.
Rose was also pleased.
"My iron play has been a bit sharper and when I have missed a green my short game has been on point," said the Englishman.
"That’s what I’ve most been pleased about heading into next week, how the short game’s looking.
"For me (this week is) about getting a bit clearer on my shots, visualizing them a bit better, getting a bit more committed to my shots.
Three-times Masters champion Phil Mickelson triple-bogeyed the 18th, hitting two balls into the water to fall six strokes behind.
"I didn't strike it very well but I putted phenomenal to stay in it," Mickelson said. "Today was an off day."
The Houston winner will earn the last spot in the Masters, if not already exempt, and Hossler is among those dreaming of a late ticket to the year's first major.
"I've been a little bit more aggressive with my wedges so far and been able to get some really makeable birdie putts, some of them inside a foot, so that's been great," said the 23-year-old from California.
He has not finished better than seventh in 25 starts on tour.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
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