Half the field had to complete the first round Friday after a long weather delay had disrupted play Thursday. All but six players were able to finish 36 holes Friday, with Branshaw recording a 10-under 134.
This is the first 36-hole lead of Branshaw's PGA Tour career.
Six players are tied for fifth at 137. First-round leader Briny Baird shot a 78 and fell into a tie for 28th place at 141.
Duval, who once was ranked No. 1 in the world, is playing in his first tournament since February.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys