Mahan, who is seven-under 135 overall, captured the WGC Match Play event and Houston Open earlier this year and is seeking to become the first player to register three wins for the season.
Seven birdies and a lone bogey catapulted the American up the leaderboard, two clear of compatriots Robert Garrigus (67) and Jimmy Walker (69), and Zimbabwe's Brendon de Jonge (69), who are at 137. Woods is three shots further adrift on two-under.
"I hit a lot of good shots. I hit so many fairways and greens, I made it easy on myself," Mahan said.
"This is a pretty punishing golf course if you get off line a little bit but I put myself in some great spots to make putts."
Mahan birdied the first but a bogey on the next halted his momentum until he picked up shots on four of his final six holes on the front nine to ensure his went out in 32.
A string of six pars followed before he sandwiched a clutch par save on 17 with birdies on the previous hole and the difficult last to pad his advantage out to two shots.
Woods is tied 11th at the halfway mark after a solid three-under 68.
On a scorching day in Bethesda, conditions again proved tough for a majority of the field but Woods remained cool under the pressure, despite likening the layout to that of a Major championship.
"It's playing like a US Open, it really is. It's quick, it's dry. You shoot something in the 60s and I think that would have been a good score," the former world number one said of the difficulty.
"I shot 68 today, which was a very good score. I'm only five back and I'm right there.
"I was just trying to stay patient the whole day. That's why I train, that's why I run all those miles. If you're carrying a little bit of body fat, it's going to be a little insulation out there.
"This is when fitness does help, and I figured that's one of the reasons why I've had the success I've had in the elements."
Woods started on the back nine and opened with six straight pars, two of which were impressive saves, before eagling the par-five 16th by sinking a 40-foot putt and celebrating with a trademark fist pump.
His excitement was tempered on the first, where he carded a bogey five after twice finding the rough and missing a six-foot par putt.
A birdie putt from a similar distance on the fifth took him back to two under for the day before a pinpoint wedge approach on the eighth to within three feet put him in prime position to mount a weekend charge.