With the punishing winds that created havoc on Friday giving way to calm conditions, the Blue Monster course lost much of its bite allowing emboldened golfers to attack the pins.
Reed, who had a share of the four-way overnight lead, fired a three-under 69 to secure a two-shot advantage over compatriots Jason Dufner (68) and Hunter Mahan (71) into Sunday.
The 23-year-old, however, might be looking a little further down the leaderboard where Woods is one shot further back after a sizzling 66 left the world number one well-placed to make a run at an unprecedented eighth WGC-Cadillac title.
"That's fine. I've seen Tiger a lot on the driving range," said Reed, when asked how he would feel see Woods in his Sunday red shirt in front of him. "Never had the opportunity to play with him and I still haven't been able to play with him.
"But you know, whenever he's close to the lead, he's a guy you have to watch out for.
"At the same time, I have to go and just play my own game."
After a gruelling second round described as a survival test, smiling players basked in nearly ideal conditions on Saturday under a brilliant south Florida sun.
While no golfer produced a round in the 60s on Friday, nine did on Saturday with 27 breaking par compared to three a day earlier.
Woods was six behind the leaders when play began on Saturday before he mixed eight birdies with two bogeys to get to one-under for the tournament.
"It was nice to get back in the tournament again," smiled Woods. "I held it together yesterday, a long day, a long, tough day and that gave me a chance today.
"I figured, hey, I'm only six back, that's definitely do-able, especially with the conditions and how difficult this golf course is playing.
"If I just get back to even par for the tournament, I'll be right there and I did one better."
The 14-time major winner carded birdies at the first and third and while he made bogey at the fourth, the world number one continued to claw his way up the board with two more birdies at five and nine.
His rally continued through the turn with back-to-back birdies at 11 and 12 that brought out a Woods' fist pump.
A bogey at the 13th was only a hiccup as he nailed a 35-foot birdie on 15 followed by another at 16 that put him a one-under alongside Briton Jamie Donaldson (71).
In contrast to Woods' blazing start, Reed sat on one over through seven holes until catching fire with an eagle on the par five eighth which was followed by birdies at 10 and 11.
A bogey at 15 would be his only mis-step on the back nine and that was quickly offset with one more birdie at the 16 to leave him on four-under 212.
"If you have a 54 hole lead, that means you're playing the best golf of the group through three rounds," said Reed.
"The thing is, I just can't get ahead of myself and tomorrow is Sunday but at the same time it's another round of golf."
Phil Mickelson also mounted a thrilling charge with a blazing back nine that featured five birdies to card a three-under 69 that left the 2009 champion at two-over.
Australian world number two Adam Scott, who had a chance to replace Woods at the top of the rankings with a win at Doral, saw his chances of victory dim with an even par 72 to leave the Masters champion on four-over.
Rory McIlroy, who had briefly held the lead, made a bogey at the third that started a slide which included double-bogeys at eight and 10 which left the Northern Irishman with a three-over 75 and seven off the pace.
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