Wiebe, a two-time winner on the PGA Tour, closed with a 5-under 67 for a tournament record 18-under 198 total on the Prestonwood Country Club course. He beat Dana Quigley by four strokes to take the $300,000 first-place check.
"Setting a record blows me away," said Wiebe, who broke the mark of 17 under set by Craig Stadler in 2004. "It's been 21 years and that's a long time. That's three kids worth. I have a great feeling of accomplishment.
Wiebe matched Bobby Wadkins as the tour's youngest winner at 50 years, 10 days. He also became the first player to win on a sponsor exemption since Christy O'Connor Jr. in the 1999 State Farm Senior Classic.
"I've been hitting the ball well the past couple of months," Wiebe said. "I didn't think I'd score 18 under. I had quite a week."
Mark McNulty was the last player to win in his first Champions Tour start, taking the 2004 Outback Steakhouse Pro-Am. Wiebe also became the second player to win the SAS Championship in his tour debut. D.A. Weibring accomplished the fear in 2003.
Wiebe, who made only $20,535 in 11 Nationwide Tour events this year, qualified for the Constellation Energy Senior Players Championship in Baltimore on Oct. 5-7.
Quigley shot a 69. Two-time SAS champion Bruce Lietzke and Keith Fergus had 67s to tie for third at 13 under, and McNulty (67) followed at 12 under.
Wiebe started the day one shot ahead of Quigley at 13 under, but dropped a stroke on the opening hole - his first bogey of the week. Wiebe countered with a 25-foot birdie putt on the par-3 third hole.
Quigley, who played in the final group with Wiebe, bogeyed the par-4 fourth and could do little to make a serious run at the winner.
"Mark hit the ball well and putted great. That's a good combination," Quigley said. "To shoot 18 under on this course is unbelievable."