Weibring shot a 5-under 67 and finished at 18-under 198, one stroke off the tournament record.
Haas posted a 9-under 63 to take second at 199. After Haas completed his final round, Weibring had three holes to make up two shots.
The charge started at 16 when Weibring rolled in a seven-footer for birdie. He hit his tee ball at the par-three 17th to three feet and sank that putt to match Haas at 17-under par. He made a 10-foot birdie putt at 18 to clinch his fourth win on the Champions Tour and first since 2005.
Mitch Adams also had a 63 Sunday to tie for third place at 16-under 200 with John Harris, who shot a 66 in the final round.