Kaymer followed his record-tying 63 on the Stadium Course on the TPC Sawgrass with a 3-under 69, capping off his round by hitting a pitching wedge to 3 feet on an island green with a back pin on the 17th hole.
He had a one-shot lead going into the weekend as he tries to end more than two years without a victory.
"Everything is coming together nicely," said Kaymer, a former PGA champion and world No. 1.
Spieth, in his first big tournament since his runner-up finish at the Masters, hasn't shown any signs of a letdown. He pieced together another bogey-free round and converted pure swings into tap-in birdies on consecutive holes on the back nine that carried him to a 6-under 66.
"I don't think it's going to be possible to stay bogey-free for two more rounds with the greens firming up," Spieth said, not sounding at all like someone making his Players Championship debut. "That's a nice goal to have, I think. When bogeys come, it's going to be how I rebound."
Kaymer was at 12-under 132. That matched the best 36-hole score on the Stadium Course at the TPC Sawgrass in 20 years, dating to Greg Norman's record-setting performance. Norman made only one bogey that week.
Spieth hasn't made a bogey all week -- he has gone 51 holes without a bogey going back to the third round at Hilton Head -- though he had to make a couple of tough chips look easy to keep a clean card.
The 20-year-old Texan was still on the practice range when he saw Kaymer finish at 12 under, a score that felt impossible to catch in warm, blustery weather. The grass remained soft on the golf course, however, allowing players to take aim at the flags.
Some players had no choice.
Adam Scott, in his first tournament as a married man, kept alive his hopes of going to No. 1 in the world this week with three birdies in his last four holes for a 67. That was a 10-shot improvement from Thursday and enabled him to make the cut on the number at even-par 144.
Rory McIlroy shot 42 on the front nine and appeared headed home early until making birdie on the 18th hole to salvage a 74 to make the cut.
Not so fortunate was Phil Mickelson. He missed his birdie attempt on No. 18 and had a 70 to miss by one. Mickelson now has missed the cut in the two biggest events of the year -- the Masters and The Players.
"I don't feel bad about the game," Mickelson said. "But mentally, I'm just really soft right now."
Kaymer is winless dating to the HSBC Champions in Shanghai at the end of 2011. The more good scores he sees, the more often his name is on a leaderboard, the more confidence he gains. Darren Clarke watched it for two days, referring to him as a "finely tuned engineer."
Even so, the 29-year-old German is hesitant to look beyond the next day. He knows it's tough to follow a record-tying round with anything remotely close. So he lowered his expectations, figuring anything around par would be suitable, and then kept his distance from the field.
"Yesterday was just a very special day for me," he said. "Even though I shot 9-under par yesterday ... if people want to talk negative about it, I then shot six shots worse. But you can always go in the negative. I see very positive things that I backed up that 9-under par with another decent round."
Spieth was even better.
He had to scramble for par from short of the ninth green and from behind the 10th green. He hit his stride in the middle of the back nine with two shots that were nearly identical -- a 6-iron on the par-3 13th that rode the ridge down to about 4 feet, and a 6-iron from 184 yards on the 14th to 3 feet.
"It was a nice break to land and roll to pin-high, because it was a very tricky pin with quite a bit of slope around the hole," he said.
Spieth has said he was proud of how he played the final round of the Masters, even with a two-shot lead with 11 holes to play. His game looks every bit as solid at Sawgrass, a course he had only seen while playing a junior event. He finished second in that one, too.
And that's what keep him going. Asked he if was getting bored being in contention so much, he smiled and said, "No, because I haven't won one."
"You should probably have to win every time in order for it to get boring," he said. "But not even Tiger gets bored."
Russell Henley didn't make a par over his last six holes -- three bogeys, three birdies -- for a 71 and was in third place at 8-under 136. Sergio Garcia (71), U.S. Open champion Justin Rose (71), Gary Woodland (71), Lee Westwood (71) and Jim Furyk (68) were six shots behind.
The course appeared to be getting slightly firmer by the end of the day. The excitement figures to start on the weekend.