Singh posted his second successive round of four-under-par 67 to stand second, two shots behind unheralded Daniel Chopra of Sweden, who birdied seven of his last nine holes to match his opening 66 for 10-under-par 132 as gentle conditions led to more low scoring at Cog Hill.
Stewart Cink made six birdies without a bogey on the front nine to tie the tournament record of 29 and birdied three more holes against two bogeys on the back for 64. Cink was tied for third at 135 along with fellow American Joe Ogilvie (69) and South African Trevor Immelman (66).
Mickelson and Woods, both returning to competition after stumbling badly at last month's U.S. Open, were again the focus of the largest galleries.
Woods showed the benefit of working overtime at the practice range by shooting four-under 67 after his opening 72. Mickelson slumped to 74 after his first-round 67.
Trying to shed the rust from taking a long break from golf following his father's death in May, Woods spent more than two hours on the range working into the night after his late-day tee time in Thursday's opening round.
"We had to organize a bunch of things," Woods told reporters. "Today I drove it great, hit my irons better."
Mickelson went in the opposite direction, the beefy lefthander had four consecutive bogeys from the second hole.
Mickelson, who did not hit a fairway until the eighth hole, did not blame any one aspect of his game. "Nothing in particular," he said.
"Just three-putt one green, and drove it in the hazard the next hole, and missed a six-footer for par on the following. Things kind of didn't go my way at all."
Singh, who broke a victory drought of more than 10 months by winning June's Barclays Classic, sank some long putts to stay close to Chopra. "I scrambled really well," he said.
The 32-year-old Chopra, one of the tour's busiest players in his 20th event of the season, is looking for his first U.S. Tour victory.
"I feel like I have the game to win," said Chopra, born to a Swedish mother and Indian father, and raised in India by his grandparents. Chopra tied for fifth at Pebble Beach for his best result this season.
"The hardest part of winning on the PGA Tour is the mental aspect, is believing that you can," said Chopra, who holed out from a greenside bunker to finish his round.
Defending champion Jim Furyk was among six players at 136, four shots behind Chopra. Eight more players were another shot back including Davis Love, Briton Luke Donald and Australians Stuart Appleby, Robert Allenby and Stephen Leaney.
Eighty-three players made the cut, which was set at even-par 142.