Bryant sank a nearly 13-foot birdie putt on the 470-yard, par-4 18th hole after both parred the hole twice in the playoff. Seeking his first Champions Tour win, Eaks had to settle for another two-putt par from just above the green before Bryant's winning putt from beside the hole.
The 52-year-old Bryant claimed the $240,000 winner's check with his second straight win at Ross Bridge and third Champions Tour victory. He finished at 12-under 204.
Last year, Bryant closed with a 64, overcoming a three-stroke deficit on the final three holes to beat Mark McNulty.
Bryant and Eaks shot 7-under 65s after starting the day five strokes behind Bob Gilder, who fell out of contention with a 73.
Denis Watson and Tom Kite -- who eagled the par-5 16th -- finished one stroke back at 205, while first-round leader Scott Hoch was two strokes behind.
Seve Ballesteros closed a rough Champions Tour debut with a 73, eight shots better than his second round. That still left him tied with Lee Trevino at the bottom of the 78-player field at 16-over 216.
'My game is not there,' said the Spaniard, a five-time major champion. 'I'm very disappointed with my performance, but I did the best I could.'
Ballesteros did have three birdies on the final nine holes.
Eaks, who will 55 on Tuesday, had his fourth second-place finish on the Champions Tour and second playoff loss in the past two years.
Eaks missed a 15-foot birdie putt for the win in regulation on 18 while Bryant watched, sending it to the playoff. With a shot at making it a three-way scramble, Watson's shot bounced over the final hole and then he sent a long birdie putt right of the hole. He also fell inches short on a 21-foot birdie putt on 17.
Hoch stumbled down the stretch for the second straight day, hitting four bogeys in five holes -- sandwiched around a birdie -- ending on the 15th to fall out of contention. He had a four-stroke, two-hole turnaround to lose the lead on Saturday with Gilder's eagle and birdie.