Vegas, the Venezuelan rookie who won the Bob Hope Classic in January for his first PGA Tour title, had 10 birdies and two bogeys at TPC Summerlin in the first of four Fall Series events.
McGirt, also a PGA Tour rookie, had eight birdies in a bogey-free round.
Vegas, playing in hot afternoon conditions, birdied the par-4 15th and par-5 16th to reach 8 under, dropped a stroke on the par-3 17th and closed with a birdie on the par-4 18th to get back to 8 under.
"I feel like I'm hitting the ball absolutely great, which is something fun to do," Vegas said. "But the main thing was I made a lot of putts today.
"The two greens I missed today, I missed by probably half an inch. And just putting from the fringe I three-putted both times, which was kind of ironic. It's just golf. It is what it is. You have to stay positive, and the more positive you can be the better you'll be out there."
McGirt, playing in one of the last groups of the day, made seven birdies in a 10-hole stretch from Nos. 7 to 16, then parred the final two holes to match Vegas at 8 under.
"I really didn't set a number," McGirt said. "I was just trying to make as many birdies as I could. Thursday through Saturday, all you're doing is jockeying for position so that you can make a move on Sunday.
"I knew there was a 7 under posted (by Green) before I even teed off. So you knew it was out there, and it was just a matter of staying aggressive and making some putts."
Green, the leader until Vegas overtook him in the final hour, made seven birdies. The Australian won the 2009 Canadian Open for his lone PGA Tour title
"Just no mistakes, which was nice," Green said. "No bogeys, which was pretty unusual. "I didn't hit it overly close. It was just one of those steady rounds where I just managed to pick up; there's probably three or four sort of unexpected birdies out there."
Nick Watney, a two-time winner this year, was two strokes back at 65 along with Harrison Frazar, Tim Herron, Vaughn Taylor, Steve Flesch, Matt Jones, Rod Pampling, Derek Lamely, Blake Adams, Garrett Willis and Alex Cejka. Frazar and Lamely eagled the 524-yard 16th hole.