Tom Lehman, Rod Pampling, Paul Stankowski, Tim Herron and overnight leader Kevin Sutherland are tied for second place at 6-under-par 138. Davis Love III and Mark O'Meara are one stroke further back at 5-under par.
Furyk, who started on the back nine at Poppy Hills, two-putted for birdie at the 10th, but was unable to convert for several holes. He carded six consecutive pars before birdieing the final two holes of his first nine.
'It's just been different,' said Furyk, referring to the dry conditions the first two days. 'I've never seen the golf courses this way in a lot of years playing here. I never realized how much slope there is on some of these greens. I've played here a lot when the greens were very wet, and they're usually slow. Not this year.'
The 2002 Memorial winner birdied the par-five fourth from 35 feet, his third birdie on four par-5s to that point. Furyk then faltered at the sixth with his lone bogey of the day when he was unable to get up-and-down from a greenside bunker.
Furyk responded in brilliant fashion as he birdied the final three holes to climb into the lead for the first time during the tournament.
'I made kind of a bad bogey at six,' said Furyk. 'It was nice to turn around and birdie Nos. 7, 8 and 9. A good finish today means I can go home and get some sleep tonight.'
Furyk, who grew up in Pennsylvania as a Pittsburgh Steelers fan, is paired with former Steelers wide receiver Lynn Swann in the Pro-Am.
'I wanted to be his partner if he was going to play,' said Furyk. 'I figure on my days off, I don't want to talk about golf, so I haven't quizzed him too much (about football).'
Sutherland struggled at Spyglass Hill, the second of three courses being used for the first three rounds of the tournament. He bogeyed the first, but recovered that stroke with a birdie at the next. He wrapped a pair of birdies around his second bogey of the round at the sixth.
The 39-year-old also carded bogeys at 10 and 13, while birdieing the 11th as he fell out of the lead.
Herron, who collapsed late last week to fall out of the lead at the Bob Hope Classic, carded a 3-under 69 at the Pebble Beach Golf Links, the final course being used for the tournament.
'Lumpy' as he is known, birdied the second and sixth to move to minus-5. He bogeyed the eighth, but responded with a birdie at the next to remain 2-under for his round.
Herron birdied the 11th around the turn, but dropped that shot with a bogey at the next. He completed his round of 69 with a birdie at the par-5 18th.
Scott McCarron, Loren Roberts, Rory Sabbatini, Dave Stockton, Jr., Tim Clark and Brad Faxon are tied for ninth at 4-under-par 140. Including the seven golfers at minus-3, there are 21 players within four strokes of the lead.
Defending champion Matt Gogel is in danger of missing the cut, which will come after round three, as he stands at 7-over-par 151.