Fijian Singh, the 1998 champion at Sahalee, fired a four-under-par 68 and American Leonard a 69, the pair finishing a testing day at Whistling Straits on nine-under 135.
Three-times major winner Ernie Els, who had led by two with eight holes to play, was a further stroke back in a tie for third after carding a 70.
Level with the smooth-swinging South African were first-round pacesetter Darren Clarke of Britain (71) and little-known American Briny Baird (69).
Clarke was delighted to bounce back from an ugly seven at the monster 618-yard 11th.
"That was pretty good, considering that I double-bogeyed my second hole," the Northern Irishman told reporters.
"I've been playing reasonably well for most of the year, but I just haven't been putting the scores together."
Baird, yet to win on the PGA Tour, mixed five birdies with two bogeys to hold the clubhouse lead after making the most of more favourable conditions in the morning.
For round two, the daunting par-72 layout was back to its full 7,514 yards and provided a stiffer test for the 154-strong field.
"The pins were harder and the greens were definitely firmer and faster," added Baird, who showed no sign of nerves playing in only his seventh major championship.
"I'm here trying to win my first golf tournament. If that tournament happens to be a major, then that would be a huge bonus.
"If you can lead after 36 holes, then why can't you stretch it two more days?"
World number one Woods, who opened with a three-over-par 75, birdied three of the last six holes for a 69, finishing at level-par 144.
He made a fast start in his bid to avoid missing the cut for the first time in a major as a professional, before struggling around the turn.
He reeled off consecutive birdies, hitting his wedge approach at the par-four first to within two feet of the flag and reaching the green in two at the 593-yard second.
The eight-times major winner, trying to end a run of nine majors without victory, gave himself another opportunity at the par-three third, but his birdie putt from 15 feet pulled up a foot short.
Woods then lost momentum, struggling for accuracy off the tee and putting pressure on himself to save par.
He ran up a bogey-six at the fifth 'Snake' hole, after finding water off the tee, and dropped another shot at the par-four sixth, where he failed to reach the green with his approach.
Out in level-par 36, he did well to salvage par on 10 and 11 before rallying at the par-four 13th where he holed a seven-foot birdie putt to get back to two over.
Another birdie followed at the par-five 16th, where he reached the green in two. He then rolled in a curling 15-footer for birdie at the par-three 17th to make certain of progressing to the third round.
The projected cut for the leading 70 players and ties was at one-over 145.
Woods has not missed the 36-hole cut in a tournament since the 1997 Canadian Open, 128 events ago.