"It was really dark," Wagner said.
Wagner, who had missed out on weekend play in his last seven tournaments, couldn't match the seven birdies he had in the third round on his way to a 64. He bogeyed three holes in a five-hole stretch on the back nine and never recovered.
The 54-hole leader has yet to win the Greenbrier Classic, now in its fourth year.
"The swing just left," Wagner said. "I'm furious. But given where I was a couple of weeks ago, I'll take a lot of positives when I get over this disappointment right now."
Defending champion Ted Potter Jr. (67), Pat Perez (69) and Brian Stuard (67) tied for sixth at 9 under. Among those in an eight-way tie for ninth place was Davis Love III, who earned his first top-10 finish of the year.
Walker joined four others after the Greenbrier Classic to earn spots in the British Open as the leading five players not already exempt from the top 20 in the FedEx Cup standings. He moved up to 17th. The others are Billy Horschel, Boo Weekley, Russell Henley and Harris English.
The tournament's end means New Orleans Saints coach Sean Payton can go back to his regular job after carrying the bag of friend Ryan Palmer.
"It's a good grind, good exercise," Payton said. "I thought Ryan was really patient."
Palmer shot a 71 Sunday to finish in a tie for 62nd at even par.
"It was a blast," Palmer said. "I was more relaxed. A vacation golf tournament. I wish I could have played better."