Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
Thomas, the overnight leader, was slow out of the blocks with bogeys at the 13th and 14th and two more at the 16th and 17th before a double bogey at the first.
But the world number three steadied the ship with a birdie at the third and seventh holes to card a three-over 73 that left him two strokes behind leader Patrick Reed.
"It's just one of those days where things - some of the par putts could have gone in, or I could have chipped it a little bit closer," Thomas, 27, said.
"Every single person in this tournament is going to go through a stretch where they get a bad run, especially here.
"I wasn't driving it well and then had a couple of putts that easily could have gone in that kind of stayed out, but I just stayed positive and kept fighting. I'm proud of myself for how I hung in."
The American, who has just one top-10 finish in five U.S. Open starts, is confident his game will hold up over the weekend.
"It's a better position than I've been in a U.S. Open before. Just have to stay patient and play my own game. I'm not going to worry about what everyone else is doing. I just need to stay focused," he said.
Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
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