They were at nine-under 131 on the Old White TPC course in White Sulphur Springs, W.Va.
Twenty-three golfers were within three shots of the lead, including seven at eight under.
Vegas doesn't have a top 10 finish this season, but he's looking to change that. He made five birdies during a bogey-free round Friday, including two of his final three holes.
"I feel like I'm playing great, I just haven't been able to put it all together," the Venezuelan said. "But I'm staying patient and working really hard to make it happen, and it's coming together."
Langley didn't have the same birdie explosion as he enjoyed in the first round, when he shot 62 to take the lead.
Starting his round on the back nine, Langley made back-to-back birdies on Nos. 6 and 7 and shot 69.
"Following up a round of 62 is never super easy," Langley said. "I left a lot of putts within six inches of the hole, just right in the heart. I need to be a little more assertive (Saturday) on the greens."
Langley and Vegas had a chance to make noise last week at the
Both faded in the final two rounds.
The top four finishers at The Greenbrier not previously eligible for the British Open will earn spots next week at St. Andrews, provided they are among the top 12 and ties.
"That's one of the goals for the week," Vegas said. "So we're going to try to go get it."
Woods had more trouble reaching fairways on Friday. He found the water to the right on the par-five 17th for the second straight day, hit his golf bag with his driver in disgust, then nearly holed his 97-yard fourth shot and made par.
He salvaged his under-par round with a short birdie putt on the par-three 18th. He declined interviews afterward.
Langley is looking to become the third person to become a first-time
So, too, is David Hearn, who was among those in the group at eight under. The Canadian is still looking for his first PGA Tour win in his 164th event. His best finish was second at the 2013
"This would be a great place for me to win one, but I've got 36 holes of golf (left)," Hearn said. "I'm playing great right now and I look forward to the weekend."
Hearn birdied six of his first eight holes and shot 64. He and
Sixty-seven golfers made the cut at two under. Michael Putnam had an eagle and four birdies on the back nine to make the cut on the number.