Joint overnight leader Ross Fisher (71) shares second with Thailand's Thongchai Jaidee and Francesco Molinari of Italy.
Jaidee began at the 10th with two birdies in consecutive holes from a combined distance of four feet.
Nilsson leads by one shot from Italian teenager Matteo Manassero, England's Gary Boyd, and Thailand's Thongchai Jaidee who are all on five-under.
Andrew Marshall was the top Briton, finishing six shots adrift of Jaidee.
The other three players to qualify for the Masters through the world ranking are South African Charl Schwartzel, Alvaro Quiros of Spain and Thai Thongchai Jaidee.
McDowell is two under and in a share of 30th - 10 behind Ian Poulter who is two ahead of Ross Fisher, Francesco Molinari and Thongchai Jaidee.
Jaidee, the first Thai player to win a European Tour event, carded six birdies and an eagle, with last week's winner Niclas Fasth one of five at five under.
On Saturday he carded a four-under-par 68 to move clear of 2010 British Open champion Louis Ooosthuizen (74), Thailand's Thongchai Jaidee (73) and France's world No. 187 Julian Quesne (67).
"I've dreamed for so long to win on the European Tour, " said Jaidee, who is now fourth on the European Order of Merit and top of the Asian Tour money list.
Thailand's Thongchai Jaidee fired a six-under par round of 66 to leave him in fourth on nine-under par with England's David Howell (68), Scotland's Richie Ramsay (67) and Gonzalo Fernandez-Castano of Spain (71) one shot further back.
Poulter, joint leader overnight on nine under alongside Ross Fisher, moved three shots clear of the field after two early birdies but his first bogey of the week on the fifth, after a three-putt, and another dropped shot on 10 left him level at that stage with Fisher, Kaymer and Jaidee.
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