The PGA Tour veteran, in pursuit of his 17th career victory on the U.S. circuit, played "very solid" golf on the way to a two-under-par 68 in the second round, finishing in a tie for sixth at four-under 136.
"All in all a very solid day," Furyk told reporters after moving up the leaderboard with a mix of three birdies and a lone bogey on a warm, blustery day at Firestone Country Club.
"I'm still a little mad at myself for making bogey on 18, but only two bogeys today. I played very solid. Left a couple putts out there, but I also made some really good plays."
Furyk has not won on the PGA Tour since his stellar 2010 campaign when he triumphed three times, his victory at the Tour Championship earning him FedExCup honours and the $10 million bonus.
This season has been an up-and-down one for him, featuring just three top-10s in 16 starts with his best finish a tie for third at the Texas Open in April.
Though Furyk has struggled on occasion with his short game, he believes he is on the way back and was greatly encouraged by his share of ninth place at last week's Canadian Open.
"I feel like some of the work I've been doing is paying off," said the 43-year-old American, who landed his only major title at the 2003 U.S. Open. "I played well last week at Canada.
"I haven't been scoring real well this summer, so I don't feel like I've been getting a lot out of my rounds. But I feel like I did a pretty good job of that the last two days. Hopefully it carries on to the weekend."
Twelve months ago at Firestone, Furyk had led the event from the opening round until he wound up with a double-bogey on the final hole to lose the title to compatriot Keegan Bradley by one shot.
Though bitterly disappointed at the time, he said it took him no more than a week to shake off that bitter loss and focus instead on tournaments to come.
"There's no sense in really dwelling on it," said Furyk, who is known for his unorthodox, loopy swing. "I played really well last year except for the last hole, played great up until then and then made six on the last hole. It's over.
"There are events that throughout my career have bothered me, events I thought I should have won or I could have won and I wish I could have a shot back here or a shot back there.
"Guys that dwell on that sort of thing and don't get over that sort of thing end up kind of hitting road blocks in their careers, and that's just never been an issue for me."
(Reporting by Mark Lamport-Stokes; Editing by Ian Ransom)
