The 2003 PGA Tour money leader made seven consecutive birdies to finish off a nine-under-par 64 at the Plantation Course to give him a 14-under-par 132 total.
Singh heads the 30-player field by one shot over first-round leader Stuart Appleby of Australia, who shot a six-under-par 67.
Four shots behind Singh at 10-under-par is Britain's Darren Clarke after posting a four-under-par 69.
Kirk Triplett (69) is in fourth place at nine under-par and Scott Hoch (71) is in fifth place at seven-under-par.
World number one Tiger Woods had a double-bogey, bogey start to his round, but recovered to shoot a three-under-par 70 and is nine shots behind Singh.
Defending champion Ernie Els made up for his even-par 73 in Thursday's first round by shooting a three-under-par 70 and is at three-under 143.
DISAPPOINTING START
Singh began his second round with opportunities to close the two-stroke gap Appleby had opened on the world number two in Thursday's opening round, but slipped five shots behind at the turn.
"I was disappointed with the front nine, obviously," Singh said of his outward one-under-par 35.
"I had a lot of chances. I bogeyed the sixth hole, which everybody was birdying."
After nine holes, Singh told his caddie that if he continued to play solid, he might get into the clubhouse at three, maybe four-under-par.
Singh could not have expected his long putter to awake as he shot an eight-under 29 with birdies on holes 12 through 18.
Singh's 64 is the lowest round of the championship.
"I tried too hard yesterday," Singh said of his putting in his five-under 68
"I went out there today and said 'Let's just hit your lines, not try to really make putts, just hit your lines and stroke them.'"
Needing just 25 putts in the second round, Singh continues a hot run of form that dates back to the end of the 2003 season.
In Singh's final eight starts of 2003, he finished no lower than tied for sixth, including wins at the John Deere Classic and the Funai Classic.
"I feel very comfortable out there when I'm playing," he said.
NO WORRIES
Paying no attention to Singh, Appleby quietly followed up his first-round 66 with a solid 67.
Though Appleby lost the lead, in his typical Australian way, he has no worries heading into the weekend.
"I didn't even look at the leaderboard today," Appleby said.
"Wasn't really a concern what I was doing in relation, because there's no necessity to do any of that right now.
"Vijay got on a good streak. I know what that's like. I was on that yesterday and had another one today. So it doesn't surprise me."
Appleby's own hot streak began on the front nine with four birdies in a row and then a fifth at the 10th hole.
Two bogeys on the back nine, including a wayward drive on the 14th hole that required a second tee shot, ultimately cost Appleby the lead.
The Australian said he had no plans to alter how he played the first 36 holes.
With Singh playing so well, Appleby believes he will follow suit.
"Absolutely the same as Vijay approached today," Appleby said of his gameplan for the third round.
"There won't be anything but single-mindedness to be focusing on what we do and what we do well. That's it."