Stricker drew first blood, dropping his birdie putt following a superb approach into the second green.
A par at the sixth was good enough to see the German back on level terms, before a birdie at the ninth saw him into the lead as they approached the back nine.
The American hit back at the 10th, carding a birdie to square the match.
Kaymer twice took the lead on the back nine, only for Stricker to reply immediately.
However, a birdie at 17 meant that Kaymer protected a one-up lead on the last hole.
His tee shot went down the right, while Stricker's split the fairway. Kaymer still found the green, but had left himself with a long putt for his birdie.
The pressure was relieved somewhat when Stricker went even further down the green, finding himself with a horrible downhill putt.
His effort was wide and long, leaving Kaymer with a two-putt for the victory.