Australian Michael Wright finished one shot out of the playoff to claim outright third spot on Sunday (Monday AEDT).
Tasmanian Mathew Goggin, who started the final round with a one-shot lead, and fellow Aussie Rod Pampling were among five players who shared fourth place.
After Taylor and Germany's Cejka parred the par-4 18th on the first playoff hole, they replayed the hole at the Ocean Course at Hammock Beach.
Taylor stuck his approach shot about six feet from the cup and rolled in the ensuing birdie putt.
In his first season on tour after turning 50 in March, Taylor had three top-10 finishes across August and September before his breakthrough this weekend.
"I just wanted to finish strong and not give it away or do something stupid and lousy," Taylor said.
The American began the day three shots behind Goggin, who had to qualify for the tournament and was also aiming for his first victory on the veterans' tour.
Taylor rolled in five straight birdies from the 10th to the 14th on his way to a 4-under-par 68 to tie Cejka at 17-under 199.
Cejka had shot his second straight round of 65 and finished his bogey-free day with a birdie on the 18th to take the clubhouse lead at 17 under.
He and Taylor had to wait and watch Australian Wright, who took the outright lead at 18 under after birdies on the 15th and 16th. Wright needed par at the last hole to win in regulation, but was forced to take a drop after two poor shots.
He failed to save bogey, which would have put him in the playoff at 17 under, and carded a double-bogey six instead.
Wright (65, 66, 69) finished alone in third at 16 under.
Fellow Aussies Pampling (64, 65, 72) and Goggin (66, 62, 73) tied for fourth with Americans Ben Crane and Ryan Armour, and Argentina's Angel Cabrera.
Taylor is projected to rise 16 spots to No.21 in the Charles Schwab Cup points race with one tournament left in the regular season. Following next week's SAS Championship, the top 72 players advance to the first leg of the three-week Schwab Cup playoffs.
Goggin may have come up short but will get a valuable boost to No.74 in the points race, giving him a chance to make the playoffs.
The 52-year-old had a one-shot lead heading into the final day after carding a tournament record 10-under 62 in the second round.
- with Reuters
