Watson's approach shot on the par-five 18th hole at Valhalla Golf Club came up short in a bunker while Eger laid up in the first cut with his approach.
After Eger got to within 9 feet with his third shot, he faltered, missing his birdie try to right of the hole. But Watson, who had blasted out of the bunker to within 3 feet, responded with a birdie putt, taking the Senior PGA Championship for the second time.
Watson claimed his 14th career victory on the senior tour as well as his sixth major championship title.
Kiyoshi Murota, the co-leader after three rounds, birdied the final hole to end at an even-par 72, grabbing sole possession of third place at minus-nine.
Irwin, who also led after 54 holes, stumbled Sunday, falling to a 1-over 73 and ending one shot further back at 8-under 280.