Furyk and Singh, both major championship winners, shot 4-under 66 at the Congressional Country Club -- a course that has played host to two U.S. Opens and one PGA Championship.
Phil Mickelson was the last amateur to win a PGA Tour event, having captured the Northern Telecom Open in 1991.
Woods -- the host of the AT&T National, who is playing for the first time since becoming a father the day after the U.S. Open -- shot a 73.
Mickelson, trying to recover from a sprained wrist and also playing for the first time since the Open, fired a 74.
The first round was completed despite a brief weather delay early in the afternoon.