Chad Campbell had a great round of his own with an 8-under 62. He joined Toms atop the leaderboard at 14-under-par 196.
Jim Furyk (70), Rory Sabbatini (67) and Charles Warren (64) share fifth place at 6-under-par 204 at Waialae Country Club.
Campbell shared the lead entering round three with Furyk. However, Furyk stumbled to three bogeys over the opening four holes to fall off the pace. Campbell and Toms, playing in the final group with Furyk, opened with back-to- back pars.
From the third through the 18th, at least one of the two men birdied 13 of the final 16 holes to run away from the field. Campbell struck first with a 7-foot birdie putt on the third.
Toms got that shot back at the next as he sank an 18-footer for birdie. They each parred the fifth before Toms forged a tie for the lead at minus-7 as he sank a 7-foot birdie attempt on No. 6.
Campbell caught fire on seven, though. He stuck his approach 4 feet from the hole and converted the birdie try. The 31-year-old then poured in a 25- foot birdie putt on the next, but Toms matched him with a 16-foot birdie of his own.
They both birdied the ninth and Campbell made the turn at 10 under, one ahead of Toms. Campbell, the 2003 Tour Championship winner, made his fourth straight birdie as he rolled in a 5-footer on No. 10.
Toms, the 2001 PGA Champion, got back within one as he rolled in a birdie putt from the back fringe at the 11th, but Campbell responded with a 13-foot birdie putt on 12 to move to minus-12.
The 39-year-old Toms then knocked his second shot to 14 feet to set up birdie on the 13th. Toms briefly joined Campbell in the lead again at 14 when he sank a 35- footer for birdie. Campbell, however, converted his 5-foot birdie try to again move one clear of his playing partner.
After both men parred 15, they made very different birdies on 16. Campbell stuck his approach within 2 feet and tapped in for birdie. He did that after Toms ran in a 75-foot birdie putt from the front fringe.
Campbell got up and down for par on 17 and two-putted for par from 15 feet at the last.
'It was a great day. Both of us played well and we kind of fed off each other,' said Campbell.
Toms also got up and down for his par at the 17th. At the last, he reached the par-5 closing hole in two. He two-putted for birdie to share the third-round lead with Campbell.
'I was just trying to feed off what Chad was doing,' Toms said. 'He was hitting the ball close to the hole. I wasn't getting it so close so I had to make a couple long putts. It was a great day all around for both of us.'
Defending champion Vijay Singh fired a 6-under 65 to move to 5-under-par 205. He was joined there by Mercedes Championships winner Stuart Appleby (69), K.J. Choi (68), Robert Gamez (66), Nathan Green (65), John B. Holmes (69), Steve Jones (68), Peter Lonard (68) and Jerry Smith (69).