Furyk bogeyed three of the final six holes at the East Lake Golf Club and still took the lead in the final PGA Tour event of the season.
His 36-hole total of 133 put him in position to win the event for the second time in three years.
First round co-leader Justin Rose finished birdie-birdie for a 68 and a two-day total of 134. Bubba Watson and Bo Van Pelt shared third place at 135, Dustin Johnson and Matt Kuchar were at 136 and world No. 1 Rory McIlroy was among those at 137.
Tiger Woods, who was tied for the lead with Rose after the opening 18 holes, had five bogeys and a double bogey in a round 73 that left him tied for 12th place at 139.
The results of the Tour Championship will determine the winner of the FedEx Cup and its accompanying first prize of $10 million.
McIlroy, a two-time winner in this year's playoff series, had the lead in the FedEx Cup points race coming into the tournament. If Friday's standings had been the final result he would have won the title.
A win in this tournament by McIlroy, Woods, Phil Mickelson, Nick Watney or Brandt Snedeker would make them the FedEx Cup champion. For any of the other 25 players in the field to win the FedEx Cup, they would have to capture this event while the five front runners in the points race finished out of contention.
Furyk, for instance, would have to win the Tour Championship while McIlroy finished 12th or lower. Rose would need a Tour Championship victory and a finish of 18th or worse by McIlroy.
"I think first and foremost, I just have to try to think of my standing in this golf tournament, not really think about anything else," McIlroy said.
"If it comes down to it on Sunday where I need to really know what I have to do for the last few holes, then of course if I have a decision to make between protecting my lead in the FedExCup or trying to win the golf tournament, I think I know what I'm going to choose."
Snedeker was tied for 10th after two rounds at 138, Mickelson was at 140 and Watney was last in the 30-player field at 149.