Singh, who fell a spot to number three in the world rankings this week, put together an eight-under-par 63 at the Westchester Country Club to tie the best opening round in tournament history.
The score also matched his best round of the year.
Jacobson shot a five-under-par 31 on the front nine and cruised into a 64, also his best opening round of the year, to finish the day two strokes ahead of South African David Frost.
Fred Couples, England's Luke Donald, Jonathan Byrd, Loren Roberts, Australian Peter Lonard, Kris Cox, Dudley Hart, Robert Damron and Roger Tambellini finished in a tie for fourth on 67.
Defending champion Jonathan Kaye finished on 73 and at 104th will need a good round on Friday just to make the cut.
Singh took advantage of a superior ball-striking round, hitting 17 of 18 greens, and subsequently made nine birdies, including a stretch of four in a row and six of eight.
"Obviously, I played really well and drove the ball really straight," Singh said.
"I attacked the golf course from the get-go with a drive off 10 (his starting hole) and just never held back," he added.
"I just played beautifully, hit a lot of shots close, which took away a lot of pressure from my putter, and when you do that you're going to shoot low."
Having won three times this year at the Pebble Beach National Pro-Am,
Over the next three tournaments, Singh had only one top-10, at the Wachovia Championship, and a tie for 59th at the Byron Nelson when he finished with a eight-over-par 78 after entering the last round just four shots off the lead.
Singh finished in a tie for 24th at last week's Memorial.
"Even last week, I had trouble timing the greens, but I was putting well," Singh said.
"My caddie kept saying 'good putt, good putt,' all day, but it wasn't going in.
"You just have to be patient enough to know that you're stroking the ball well and it's going to go in sooner or later. Just picking the right line is the key."
Singh, twice a winner of the Buick Classic in 1993 and 1995, came into the event knowing that what he had been doing the last three tournaments was not working, so he decided to use a driver from the first tee and try to play golf the old fashioned way.
It paid dividends.
"Well, last week since I wasn't making any putts, you try to creep towards the pin side and towards the short side," Singh said describing his failed strategy.
"When you're going for the flag and there's water or a hazard nearby, if you just miss it you're going to make bogeys and doubles and that's what's been happening.
"Today I just said forget it, play safe, get a plan going and hit it to the correct side of the holes."