Roberts made nine birdies and two bogeys over the demanding Westchester Country Club course.
"I just happened to have a great day with the putter," said Roberts, who has seven career wins. "I had an impossible chip-in (on No. 17) and made a couple of long putts. I just kind of got on a roll today and hit it on the right spots."
The Buick Classic serves as a valuable tuneup for next week's U.S. Open. Defending champion Sergio Garcia was at 3-under 68.
Earlier this week, Roberts failed to qualify for the year's second major, but he did not let it affect him on Thursday.
Roberts started on the back nine, playing the first four holes at 1-over. But beginning on the par-3 14th, Roberts had nine birdies and a bogey in a 12-hole stretch.
"There have been two Opens in the last 10 years that I really wanted to play in, and that was Pebble Beach and this one," Roberts said. "I'm sorry I'm not going to be in. I'm here, so I'm going to try to win the golf tournament here."
On the par-4 17th, Roberts sank a lob from 20 yards after overshooting the green on his second shot.
"I love this golf course," Roberts said. "Quite honestly, I don't think we play enough golf courses like this anymore, old and classic. I like the nuances of this course. It's pleasing to the eye and it has some quirkiness. It's up and down and around. I think it's just a great test of golf."
Kelly, who won the season-opening Sony Open in Hawaii, was on Roberts' heels after a round that included an eagle, five birdies and a bogey. Kelly held the lead entering the clubhouse before being overtaken by Roberts.
"I've said before, I don't care where I win, as long as I can win, and that's still true," Kelly said. "But, knowing that the majors are kind of where great players are measured these days, I'll take anything I can get."
Muehr had some extra motivation in the first round after winning a 12-man playoff on Tuesday in Maryland to qualify for the U.S. Open.
Like Roberts and Kelly, Muehr also started on the back nine and began with a flurry. Muehr birdied five of his last six holes on the back side after a bogey on No. 11. He added two more birdies on the front side.
"It's been a tough year," said Muehr, who has missed the cut in 11 of his 16 events. "But at the same time, I really feel like I'm playing a lot better."
The opening round also saw three aces recorded. Stephen Allan and Angel Cabrera made a hole in one at the sixth and Larry Mize the 16th.