The seasoned Indian ended his campaign with a total of nine-over 289.
On a disastrous day, Jeev stumbled to a bogey on the very first hole before dropping three more strokes to make the turn four-over.
The back-nine was no better as Jeev found bogeys on the 13th and 15th holes and though he managed a couple of birdies in the next two holes, a double bogey on the 18th brought him back to square one.
Meanwhile, Tiger Woods won the title for a record seventh time, overhauling Padraig Harrington with a sizzling burst of scoring before benefiting from a late collapse by the Irishman.
The American world number one fired a five-under-par 65 on a hot and humid day at Firestone Country Club to clinch his 70th PGA Tour victory, and fifth of the year, by four strokes.
Woods took control by covering the front nine in a spectacular five-under 30 on the way to a 12-under total of 268.
Harrington, who had led for the first three rounds, regained a one-stroke cushion with three holes to play before his title bid unravelled with a triple-bogey eight at the 16th.
A closing 72 earned him a share of second place with Australian Robert Allenby (66).
The final round, however, boiled down to a mouth-watering duel between playing partners Woods and Harrington in front of huge galleries.
Trailing by three shots overnight, Woods clawed back two of them at the par-five second where he conjured a brilliant eagle.
After hitting his second shot from the middle of the fairway to 24 feet, he coolly sank the curling right-to-left putt before raising his putter into the air in celebration.
