Canada's Silverman, seeking a first US PGA Tour title, shook off an opening bogey at the 10th hole of the Tahoe Mountain Club course, where he birdied seven of his last nine holes to rocket to the top of the leaderboard.
At the par-four first, his 10th hole, his 191-yard second shot left him less than foot for birdie, and he notched his last points of the day with a 22-foot birdie at the eighth.
Silverman said he tried not to focus on the Modified Stableford scoring format, which awards points for birdies and eagles and subtracts them for bogeys and worse.
"You try to put the points out of your head and just focus on making birdies and adding up your score normal," said the 36-year-old ranked 120th in the world.
"You get rewarded for birdies and the points kind of take care of themselves."
Kraft also had an early bogey, at the second, but he was promptly back on track with an eagle -- worth five points -- at the par-five third.
He had two more birdies and a bogey on the front nine and five birdies coming in.
Kraft said the scoring system was "kind of weird," but noted: "You're still just going to go out and try to shoot the lowest score."
American Nate Lashley was in third place with 15 points after a round that included eight birdies and a bogey.
American Sam Ryder and South Korean S.H. Kim were tied on 14 points in the tournament that is being played opposite the British Open, the final major championship of the year, at Royal Troon, in Scotland.
