Kaymer, trying to become the first player to win three European Tour events in a row since Tiger Woods in 2006, birdied the first while Parry - five clear at one point at Carnoustie on Saturday - bogeyed it.
They were both 12 under par as a result, with Spain's Alvaro Quiros two back in third after he also started with a bogey five.
Lee Westwood, needing a top two finish to replace Woods as world number one, parred the first two and remained in a tie for fifth.
Parry matched Kaymer's 15 foot birdie putt on the long fifth, but the US PGA Championship winner nosed in front again by pitching to within 18 inches of the cup at the sixth and moving to 14 under.
By then Westwood had slid back to only joint ninth by parring the first six holes to remain eight under.