Bradley opened the tournament with a course-record 60 at the TPC-Four Seasons Resort course and although he was unable to post another low score he was able to fight off a series of challengers.
His two-day total of 11-under 129 was one shot off the tournament's 36-hole record. He is seeking his second win at the Nelson and his fourth on the tour in a career that includes a victory at the PGA Championship.
Tom Gillis recorded a 7-under 63 and Sang-Moon Bae had a 66, leaving them tied for second at 132. Former Masters champion Charl Schwartzel shared fourth place with Ryan Palmer and 2012 PGA Tour rookie of the year John Huh at 133.
It took a score of even-par 140 to make the cut and defending champion Jason Dufner barely made it with two rounds of 70.
Temperatures soared into the 90s Friday as the region endured its first blast of summertime weather.