Langer had led going into the final round but Haas shot a 6-under-par 65 to Langer's 69, deadlocking them at 14-under 199 and forcing a playoff.
The winner collected $255,000 for his second victory on the tour. His other win was at the Administaff Small Business Classic last year.
Haas, the Toshiba defending champion, was trying for his 11th Champions win.
Curtis Strange and Tim Simpson were another shot back.