"He's always been a really good putter," said Dustin Johnson, who shot 69 to finish at 138, 8 strokes back. "So obviously he's making a lot of putts, and to make putts you have to be hitting good shots. I think obviously, 10 under, his score speaks for itself, he's doing everything well."
Kaymer had his struggles with the game soon after reaching No. 1 in the world. He attempted to change his swing to help him hit a draw, a shot he felt he needed to compete at the highest level.
Before his Ryder Cup heroics, he was playing so poorly that there was talk about him giving up his spot on the team. He won later that year at a limited-field event in South Africa, but when he won the Players last month, it was his first significant victory since the 2011 HSBC Championship. Before that, he had fallen outside of the top 60 in the world.
"It's just very, very satisfying," Kaymer said. "I said to my caddie [Craig Connelly], there were a couple of shots today that I was surprised how good they were. Because I was not expecting to hit it that close, because it was a tough pin and all of a sudden you end up with a very good birdie chance and you would have taken 4 from the fairway.
"So I'm just hitting the ball very solid right now, and I think it's important to keep going and not try to relax. There's still a lot of stuff to improve on, but the way I played now is quite nice."
What appears to be a one-man tournament has a group of players with at least some hope heading into the third round. Todd, who won the Byron Nelson Championship last month for his first PGA Tour win, will play in the final group Saturday in his first U.S. Open.
Brandt Snedeker had a 68 and joined Na at 3-under 137.
Brooks Koepka, the American who is carving his way through the European Tour, birdied his last hole for a 68 and joined the group at 2-under 138 with Brendon de Jonge (70), Henrik Stenson (69) and former PGA champion Bradley, who played in the same group with Kaymer and rallied for a 69.
The Associated Press contributed to this report.