American Watney fired a two-under-par 69 and Spaniard Garcia a 68 on the difficult, fast-running Bethpage Black layout to end a blustery afternoon at eight-under 134.
Fijian former world number one Vijay Singh, relishing being pain-free after three years of assorted health problems, was a further stroke back after carding a 67, level with American Bob Estes (66).
The ominous figure of Woods was at five under, the American world number three having recovered from a bogey-bogey start to shoot a 69 in pursuit of his fourth US PGA Tour victory this year.
Woods said he had hurt his back sleeping on a soft hotel bed overnight, and that he had to grit his teeth through pain throughout his round.
"It hurt all day," Woods said after making four birdies in his last 15 holes. "I didn't feel very good. It didn't hurt standing up or at the bottom of a squat but somewhere in between it was going to catch.
"It would grab just before impact so I'd kind of expect it, I could kind of get through that. I've done that kind of stuff before so I know what it feels like."
Woods lipped out with a birdie putt from 16 feet on his final hole, the par-four 18th, but was overall happy with his position going into the weekend.
"I'm only three back so I'm right there," said the American, who led the points standings this week coming into the first of the US PGA Tour's four lucrative FedExCup play-off events.
Watney was also delighted to be in contention as he seeks his first victory on the US circuit since the AT&T National.
"It's been a little while since I've been in this position, and it feels good to be back," said the American, who briefly led the elite field by two shots before bogeying two of his last three holes. "I'm really excited for the weekend.
"I felt pretty good. I hit the ball very nice all day, and it was weird, I made some really nice putts and I had some three-putts. Kind of a live-by-the-sword, die-by-the-sword type of day."
Garcia, who ended a four-year title drought on the US PGA Tour by winning the rain-delayed Wyndham Championship on Monday, was happy to have played well in the tougher conditions of the afternoon.
"Definitely a nice round," said the Spaniard. "Yesterday was a very nice round but it was playing easier than today. The greens were very, very firm out there, so it was difficult to hit it close to some of the pins, even from the fairway."
Overnight leader Padraig Harrington of Ireland endured a difficult day, bogeying five of his first eight holes on the way to a 75 and a three-under total.
US PGA Championship winner Rory McIlroy, the world number one who was grouped with Woods in a glamour pairing for the first two rounds, battled to a 73 to make the cut by just one shot.
The cut fell at one-over 143 with US Open champion Webb Simpson, 2003 US Open winner Jim Furyk and Keegan Bradley, who won his first Major title at last year's 2011 US PGA Championship, among those failing to advance.
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