Their 36-hole total at Castellon, Spain, 12-under-par 130, leads India's Shiv Kapur (65) by two strokes.
Defending champion Sergio Garcia, a Castellon native and the first-round leader, was 10-under through 15 holes when Friday's play was suspended by darkness.
The suspended first round featured 40 mph wind gusts, causing the round to be completed early Friday morning.
"(The wind) does not affect my swing, but I was in a lot of pain the last few holes," said Kaymer, who has missed nine months with a foot injury. "The doctor told me to avoid long walks and that I won't be 100 percent for a year."
This year's Masters champion, Angel Cabrera of Argentina, was disqualified Friday after missing his tee time.
2014: The Year in Music [PHOTOS]