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Resuming on four under, Lowry birdied four of the opening five holes and picked up another two shots on eight and 10 to move to 10 under.
Overnight leader JB Holmes consolidated his challenge with a 68 to move to eight under.
"You can have that great round and that day where everything goes right," said Holmes. "But it's nice to get two rounds in a row. It shows a little consistency."
English duo Tommy Fleetwood and Lee Westwood are just one shot further back on seven under, while world number one Brooks Koepka also kept himself in the hunt for a fifth major on five under.
However, Woods was made to pay for his disastrous 78 on Thursday as a one under par round left the 15-time major champion still on six over and five shots off the projected cut.
"It's more frustrating than anything else because this is a major championship and I love playing in these events," said Woods, who has struggled at three majors since his stunning triumph at the Masters in April.
"I love the atmosphere. I love just the stress of playing in a major. Unfortunately, I've only had a chance to win one of them and was able to do it. But the other three I didn't do very well."
Fleetwood played a starring role in Europe's victory at the Ryder Cup last year and the world number 20 has a chance for his first major heading into the weekend as he birdied the last for a round of 67.
"I'm happy that I had a chance to scrap today and actually did really well. Was up to the test and, again, did a lot of good stuff," said Fleetwood. "Overall, two really good rounds of golf to start."
Westwood rolled back the years with four birdies on the back nine to shoot into contention with a 67.
Justin Rose is another Englishman in the mix as an eagle on the 12th moved the world number four to six under.
Koepka has not finished outside the top two in all three majors so far this season and the American is dangerously poised after moving to five under with another solid round of 69.
But the PGA champion was left frustrated he has not hit the front yet due to his putting.
"I haven't made a putt all week, so I just need to figure that out," he said.
"If I can just make some putts I could have very easily been 10-under and maybe more."
Three-time major winner Jordan Spieth is also five under after storming up the leaderboard by picking up five shots in four holes between five and eight.
Woods raised hopes that he could recover from a difficult opening round with his troublesome back restricting his movement in cold conditions.
The American was two under for the day after six holes, but a bogey at the seventh stalled his fightback.
Back-to-back birdies at 10 and 11 gave Woods hope again but a bogey-bogey finish was a fitting end to a frustrating two days for the 43-year-old.
Home favourite Rory McIlroy also has a huge task to stay around for the weekend as he tees off after shooting eight over in his first round.
