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After seven straight pars on the front nine, Walker ran off five birdies down the stretch, including a 17-foot putt on the par-3 18th.
Walker is hoping to secure a spot in the British Open in two weeks. After the Greenbrier Classic, the leading five players not already exempt from inside the top 20 in the FedExCup points standings will earn a spot at Muirfield. Walker is 24th.
"I have a room booked," Walker said. "I might as well go use it."
Sweden's Jonas Blixt was four strokes behind Wagner at 10 under after shooting 67. Australians Matt Jones (66) and Steven Bowditch (69) and Texas teenager Jordan Spieth (67) were at 9 under.
Spieth overcame two early bogeys with birdies on three of the final four holes.
A win would give him his PGA Tour membership and make him eligible for the FedEx Cup playoffs. He's won more than $1.1 million this year and is assured of a tour card when the new season starts in October.
Among six golfers at 8 under included Bill Haas, the winner at Congressional a week ago.
Second-round leader Matt Every bogeyed the first two holes and quickly fell off the leaderboard. He shot 74 and fell into a tie for 27th at 5 under.
Ten players were trimmed from the field after Saturday's round; 81 players had advanced after Friday's play.
|Atlanta - LP: J. Walden||4||FINAL|
|Chicago Cubs - WP: H. Rondon||5|
|Washington - LP: J. Zimmermann||2||FINAL|
|Philadelphia - WP: A. Burnett||6|
|Chicago WSox - LP: H. Noesi||4||FINAL|
|Cleveland - WP: C. Kluber||7|
|NY Yankees - LP: A. Warren||2||FINAL|
|Baltimore - WP: T. McFarland||3|
|Pittsburgh - LP: T. Watson||5||FINAL|
|Cincinnati - WP: C. Partch||6|
|Miami - LP: H. Alvarez||1||FINAL|
|NY Mets - WP: Z. Wheeler||7|
|Toronto - WP: A. Loup||8||FINAL|
|Tampa Bay - LP: G. Balfour||5|
|LA Angels - WP: G. Richards||3||FINAL|
|Texas - LP: N. Tepesch||0|
|St. Louis - WP: P. Neshek||7||FINAL|
|Milwaukee - LP: F. Rodriguez||6|
|Boston - WP: J. Lackey||8||FINAL|
|Houston - LP: S. Feldman||3|
|Detroit - WP: A. Sanchez||2||FINAL|
|Kansas City - LP: D. Duffy||1|
|Minnesota - LP: K. Johnson||2||FINAL|
|Colorado - WP: J. De La Rosa||6|
|San Diego - WP: J. Hahn||6||FINAL|
|Los Angeles - LP: D. Haren||3|
|Oakland - LP: J. Samardzija||2||FINAL|
|Seattle - WP: F. Hernandez||3|
|Arizona - LP: M. Bolsinger||0||FINAL|
|San Francisco - WP: T. Lincecum||5|
|Brt Columbia||8:30 PM|
|Edmonton||7/17/14 7:30 PM|
|Toronto||7/18/14 6:00 PM|
|Hamilton||7/18/14 9:00 PM|
|Montreal||7/19/14 6:00 PM|