Branshaw, in his third year on the PGA TOUR at age 37, finished 10-under 134 and is looking for his first career win.
Bill Haas and 2001 champion Cameron Beckman are a stroke back and J.P. Hayes is alone in fourth at 8-under. Eighteen golfers were within four strokes of the lead and eight others were another stroke back when play was suspended by darkness at 7:15 p.m.
Six golfers were left on the course and second-round play at Annandale Golf Club will begin at 7:45 a.m. Saturday.
After setting an opening-round record with a 63, first-day leader Briny Baird fell to 3 under with a 6-over 78.
The cut was at even par when play stopped, but Saturday morning's finishers could change that. Play fell behind in the tournament after lightning forced a delay of nearly three hours Thursday.
Branshaw played a bogey-free round of 4-under. He hit a 25-foot putt on the 17th hole to move into a three-way tie for the lead, then sank a 5-foot putt on 18 to take the lead alone.
Haas was among 55 golfers still on the course when play was stopped Thursday. He made eight birdies in 26 holes Friday morning and had a bogey-free 67 in the second round.
Beckman overcame two bogeys and a double bogey with six birdies to finish at 2-under 70 after an opening-round 65.