The former Arizona State star shot 8-under-par 63 on Friday to take a three-shot lead before darkness suspended play at the FBR Open.
Quinney, a PGA Tour rookie after five years on the Nationwide Tour, is at 13-under 129 through 36 holes at TPC Scottsdale.
Billy Mayfair and Bart Bryant were three shots back after 66s.
Mayfair hasn't won on the tour since 1998 and is coming off a difficult year that included a divorce, surgery for testicular cancer and his mother's stroke.
But his game has been terrific this week on a course that's just a few hundred yards from his home.
He chipped in from 85 yards for an eagle on the 552-yard, par-5 15th hole to reach 11 under before his only bogey of the day on the 18th.
"I hope an old guy wins once in awhile like myself," the 40-year-old Mayfair said, "but it's good to see these young guys come off the Nationwide Tour and start playing well immediately out here, because that's what that tour is for."
Bryant, finishing just before darkness fell, made a birdie on his final hole, the 464-yard, par-4 ninth.
John Rollins and Robert Garrigus and former Georgia golfer Bubba Watson were four back at 9 under.
Among the 18 players on the course when play was suspended was Augusta native Charles Howell, who was 9 under with two holes to play.
Howell, who already has two runner-up finishes this season, bogeyed his first hole on Friday, then birdied Nos. 2, 5, 6, 9, 13 and 15.
Augusta's Vaughn Taylor is also in the thick of things. He shot his second consecutive 67 and is 8 under. Taylor had seven birdies and three bogeys in his second round.
Two-time FBR Open champion Phil Mickelson is expected to miss the cut this morning when the second round is completed. The two-time Masters Tournament champion had 69 on Friday and is 1 under for the tournament. The cut is expected to be at 2 under.
In two starts this season, Mickelson tied for 45th at the Hope Classic and tied 51st at last week's Buick Invitational in La Jolla, Calif.
He has not finished better than tied for 16th since his 18th-hole collapse at last year's U.S. Open.