Chapman's round was his worst of the week, but it didn't derail his victory bid after entering Sunday's final session with a 5-shot cushion.
He bogeyed the final two holes, ending at 13-under 271, but still beat John Cook, who fired a 2-under 69 to grab sole possession of second place at minus-11.
Four-time Senior PGA winner Hale Irwin ended with sole possession of third place one shot further back after posting a 3-under 68.
Tied for fourth at minus-9 were Peter Senior (8-under 63) and Sandy Lyle (7-under 64).
Ninth-place finisher Kenny Perry carded the lowest round in Senior PGA Championship history Sunday, a 9-under 62 that included eight birdies, one eagle and one bogey.
Perry ended at 8-under 276.