Robert Allenby, Miguel Angel Jimenez and two-time Masters winner Bernhard Langer are tied for third place after opening rounds of 5-under-par 67 at the Stadium Course at the TPC at Sawgrass.
'I needed to go out there and see him,' said Woods. 'Hopefully I turned his spirits around and made him feel a little bit better. Hopefully everything will be positive from here on out.'
Woods struggled on Thursday as he only managed an even-par 72 and is tied for 67th place.
Woods mixed five birdies and five bogeys and was 1 over par until a birdie at the par-5 16th. He missed that fairway and hit only half of them on Thursday.
'At least I pieced it together coming in,' said Woods. 'I hit some good shots coming in and finally figured out my putting stroke. Last week I didn't putt very good, but at least today I found something.'
Woods will have a lot of catching up to do if he is to catch the co-leaders. Love and Furyk were paired together on Thursday and Wednesday night, Furyk and his family hosted a dinner for Love, Phil Mickelson and Justin Leonard and all of their families.
Love broke into red figures at the par-5 second hole. He hit a 4-iron to 9 feet, but two-putted for a birdie. Love, the 1997 PGA Champion, seemed to be in trouble at the par-3 third, but he holed a clutch 15-foot par save.
Love started his move up the leaderboard with sharp iron play. At the sixth, Love hit a 9-iron inside 3 feet to set up birdie. He made it two in a row with a 5-footer at the par-5 ninth.
He kept it going around the turn as he parred No. 10, but two-putted for a birdie at the par-5 11th. Love hit a sand-wedge to 10 feet at the 12th and converted the birdie putt to reach 6 under par for the championship.
Love got it to 7 under at the par-5 16th. He drove into the rough, but after a pair of sand-wedge shots, Love drained a 7-footer for birdie. He parred out for his lowest opening round at Sawgrass.
'It was all in all a good day,' acknowledged Love, who fired a final-round 64 to come back and win this title in 2003. 'When you come to a place like here, it gives you a lot of confidence. It's nice when you get off to a good start like I did today.'
That victory was part of a spectacular year for Love when he won four events. Love has not won since The International in 2003, but feels strong enough to return to the winner's circle.
'It's always frustrating when you don't win when you have a chance,' admitted Love, who also won this event in 1992. 'I know what I have to do to do it. I know I'm going to win soon.'
Furyk did not fly out of the gate on Thursday. He parred his first seven holes until a 20-foot birdie putt at the eighth. He rolled in a 23-foot birdie putt at nine, then really took off on the second side.
At the par-5 11th, Furyk hit a hybrid club to 16 feet and two-putted for birdie. He recorded back-to-back birdies at 13 and 14, then sank a 4-foot birdie putt at the 16th.
Furyk took advantage of Sawgrass' signature hole, the island green, par-3 17th. He hit a three-quarter 8-iron inside 5 feet and rolled home the birdie try to reach minus-7.
'There's times when you can get off to a start like that, look up on the board and see guys getting off to a good start. You want to go out and try to force things and try to make some birdies,' said Furyk, who won the 2003 U.S. Open. 'I stayed patient and just let it happen,'
World No. 2 Vijay Singh, two-time Masters winner Jose Maria Olazabal, Pebble Beach champion Arron Oberholser, Ben Crane, John Rollins and Bo Van Pelt are knotted in sixth place at minus-4.
Retief Goosen, the third-ranked player in the world, shot a 3-under-par 69 on Thursday. Mickelson finished one shot worse with a 70 and Ernie Els carded an even-par 72.
Defending champion Fred Funk managed a 2-under 70.