Kirk followed up his 5-under 65 on Thursday by shooting a 7-under on Friday to take the second-round lead at the Detroit Golf Club. Simpson, who entered the event No. 6 in the world ranking, shot a 64 to move into the tie.
The 35-year-old Kirk has four career PGA Tour victories, the most recent coming in 2015. He took a leave of absence last year to focus on treating his alcohol abuse and depression.
Bryson DeChambeau and Matthew Wolff are among six golfers who sit one shot back of the leaders after shooting a 67 and 64, respectively, on Friday. Mark Hubbard, Ryan Armour, Richy Werenski, and Seamus Power are also one stroke behind the leaders.