The 28-year-old Californian posted a solid one-under 71 to follow up his impressive 64 on Thursday.
Kaymer, composed and as tidy as ever, was bogey free as he shot a 70 and he looks well placed to keep hold of his top spot in the ranking given Britain's Lee Westwood -- who can return to number one with a win here -- is nine shots off the lead.
Westwood, who was grouped with Kaymer, shot two over on Friday leaving the German confident he would remain atop the rankings for some time yet.
One player Kaymer will be wary of, this weekend at least, is Molinari, who moved up the leaderboard with a four-under 68 built around some excellent work around the greens.