Jeev, playing his first tournament after being laid low by a rib injury for three weeks, sank in three birdies against an equal number of bogeys at the Firestone Country Club.
The seasoned Indian picked up a birdie on the second hole but was pulled back by a bogey on the very next hole. He gained a shot on the sixth to make the turn one-under.
His backward journey also started well with a birdie on the 10th but bogeys on the 11th and 18th holes prevented him from breaking par on the opening day.
Irishman Padraig Harrington opened a two-stroke lead at the top after carding a flawless six-under 64. "I'm very happy," Harrington, 37, said after posting his lowest score of the year. "It was nice to shoot a score that probably was even slightly ahead of how I played.
"I haven't been doing that too often this year. I had plenty of birdie chances where I holed a couple of putts that really turned a 67 into a 64.”
Thai Prayad Marksaeng, South African Tim Clark and American Scott Verplank shared the second spot.
World number one Tiger Woods and Spaniard Sergio Garcia were tied for the eighth spot after turning in identical 68s.
