Brad Faxon fired a 5-under 66 and shares third with Brian Gay, who carded an even-par 71 on Saturday. The duo is tied at 7-under-par 206, one shot better than two-time former champion Vijay Singh (69), John Senden (72) and Kenny Perry (72).
The Irishman struggled after the birdie at 10. He three-putted from 18 feet for a bogey, then missed the green at the next to drop another stroke.
Harrington rebounded with a 15-foot birdie putt at the 13th, but collected his third birdie of the back nine at the 15th. He chipped in for birdie at the par-3 16th to reclaim a one-shot advantage.
Furyk once again tied him, but Harrington, playing one group ahead of Furyk, two-putted from 25 feet for a birdie at the last.
'I've got to be pleased with the final score,' said Harrington, a three-time European Ryder Cupper. 'I just have a better attitude to this week, that's it. I'm probably not being as hard on myself or something along those lines. It's not nothing but that.'
Harrington finally earned his first PGA Tour victory in the United States earlier this year. He captured the Honda Classic in March when he defeated Singh in a playoff.
He thinks the breakthrough will help him come Sunday.
'After winning once on the tour, at least it's a little bit of a monkey off my back,' said Harrington. 'I didn't feel it but certainly there was. It could have been there, and that's obviously gone. It's just a chance to win my 14th event of my career tomorrow, and go out and do the same things.'
Furyk broke into red figures at the par-5 fifth when his 3-wood came up short of the green. He hit a wedge 15 feet right of the pin and ran home the birdie try.
The 2003 U.S. Open champion ran into trouble at seven. His drive found the rough, but he muscled his second to the middle of the green. Furyk misread the putt, leaving it 4 feet short, where he missed again, leading to bogey.
Furyk parred his next seven holes, then split the fairway at No. 15. He was on a severe downslope and hit his wedge approach heavy into a front bunker. Furyk blasted out to 20 feet, but missed the putt and fell to 7 under par for the tournament.
At the par-3 16th, Furyk hit a 3-iron to 10 feet to set up birdie and draw even with Harrington. The Irishman pulled ahead with a birdie at the 18th, but Furyk caught him on the same hole.
Furyk used a 3-wood for his second at the par-5 closing hole at Westchester, but dumped the ball in a greenside bunker. He played his third to 4 feet and he rolled in for a share of the lead.
'I was very happy with the score I shot. Really, I thought the golf course played very difficult,' said Furyk. 'Obviously I'm happy with the way I'm playing. The big step is to go out tomorrow and play a good round and try to win the golf tournament and not really putting the cart before the horse.'
Furyk is looking for his first victory since the Buick Open two years ago. His next win would be his first since wrist surgery, but Furyk knows how to get it done.
'It doesn't matter what name is chasing you,' said Furyk. 'It's all about playing your style, attacking the golf course the way you want to, and I can't affect how the other guys are playing. I can only affect the way I'm playing so I don't really worry about it.'
Dean Wilson (66), Pat Perez (68), Brett Quigley (68) and Len Mattiace (73) are tied for eighth place at 4-under-par 209.
Defending champion Sergio Garcia struggled to a 2-over 73 and is part of a group tied for 48th at plus-3.