Goss was runner-up at last year's U.S. Amateur Championship, before finishing low amateur at this year's Masters.
He missed the cut at last week's Travelers Championship in his pro debut, but brought much better form to storied Congressional in leafy Bethesda just outside Washington DC.
Goss posted a six-under total of 136 to end the round level with fellow Australian Marc Leishman (66) and Americans Patrick Reed (68) and Ricky Barnes (69).
Goss hit only four of 14 fairways on Friday but used his recovery skills to the full as he reached 14 of 18 greens in regulation.
"I don't think I hit one fairway until the 11th ... but I scrambled my way pretty good today," he told PGA Tour Radio.
"I was able to get it up and down (for par) every time I missed the green.
"It's only my second week as a pro and being on the top of the leaderboard, it just gives you a boost of confidence.
"I didn't really have too many expectations. After last week, I was a little bit disappointed but I came here pretty fresh and open-minded. And I'm on top of the leaderboard. I couldn't be more pleased."
Reed, who has been quiet since winning the WGC Cadillac Championship in Miami in March, finished strongly with three birdies in his final five holes.
"Yesterday I hit a lot of fairways which allowed me to attack the greens but today the tee shots weren't there so I was playing a lot out of the rough (and) I had to make some smart decisions on key holes," said Reed.
He made headlines after his WGC victory when he said he belonged among the top five players in the world.
He said he was subsequently distracted, not by the reaction to his comments, but by the May birth of his first child with wife Justine.
Several big names, including Woods, Jason Day and Jason Dufner, missed the cut.
Woods, playing his first tournament since back surgery in March, was predictably rusty, especially with his short game.
Over two rounds, he got up-and-down only three times out of 16 attempts when he missed a green.
(Reporting by Mark Lamport-Stokes in Los Angeles and Andrew Both in Cary, North Carolina. Editing by Gene Cherry/Greg Stutchbury)
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