Sluman, who came into the final round three shots in back of Haas, finished at 10-under 206, winning the event for the third win in the last four years and claiming his fourth Champions Tour win overall.
Haas tumbled into a tie for second place with 3-over 75. His day included a double-bogey on No. 14 that dropped him to minus-8, where he finished along with Brad Bryant (73) and David Eger (72).
The biggest jump of the day went to Tom Pernice Jr., who climbed 13 spots to tie for fourth at 7-under 209.
Pernice shared fourth with Bobby Clampett (74), Mark Brooks (74), Mark Wiebe (70) and Steve Lowery (73).