Davis Love III, who won this event in 2000, posted a 6-under 66 to finish alone in fourth.
Tournament host Tiger Woods opened with a 68 for the third year in a row. The defending champion had an up-and-down round at Sherwood Country Club that started with a bogey at the second. He countered with a birdie at the very next hole but found trouble again with a bogey at the par-4 fourth.
Woods bounced back again in remarkable fashion with four consecutive birdies starting at the fifth. The top player in the world faltered, however, with a bogey at the ninth to make the turn at minus-2.
At the par-5 11th, Woods knocked his second shot within six feet of the hole. His eagle try failed to find the bottom of the cup and he settled for a birdie.
Woods then drained a short birdie putt at the par-5 13th on his way to a 4-under 68. Woods was joined by Phil Mickelson and Colin Montgomerie in a tie for eighth.
'It was perfect conditions to score today,' said Woods. 'If you just look at the scoreboard, you can see that. There are five par-5s, and they are all reachable with good drives. You knew you had to take it low today to keep pace.'
Furyk jumped out of the gate with an eagle at the par-5 second and followed with back-to-back birdies from the third to quickly move to 4-under. He added another pair of birdies from the 10th and reached 7-under with a birdie at the 14th.
'This course right now is not playing overly long,' said Furyk. 'If you knock the ball in the middle of the fairway and hit a nice, high, soft iron shot, you are going to do pretty well.'
At the par-3 18th, Furyk drained a 20-foot putt for birdie and the outright lead.
'You want to play a solid round and whether you are in the lead at 4-under or 8-under, you just want to put yourself in decent position,' said Furyk, who matched the course record. 'Being in the lead after the first day is really not that important. But I want to build on this, keep giving myself opportunities with my iron play and I like the way I'm putting right now.'
Chris DiMarco carded a 5-under-par 67 to finish alongside David Toms and Retief Goosen in a tie for fifth.
Mark O'Meara had four birdies on his round until a double bogey at the par-3 12th. He responded with a birdie at 13 and picked up back-to-back birdies starting at the par-5 16th before a double bogey at the last for a round of 69. Michael Campbell finished one shot further back at 2-under-par 70.
Bernhard Langer carded an even-par 72. He was followed by PGA Championship winner Rich Beem at 2-over-par 74.
Vijay Singh, who captured the Tour Championship in November, struggled with an opening-round 75 while Bob Estes was one shot further back after a 4-over 76.
This year's field consists of the top 12 players from the Official World Golf Rankings as of September 30th, plus four exemptions chosen by the Tiger Woods Foundation.
Full-field scores from the Target World Challenge