Conway, who this week was named to replace Ana Beatriz as the driver of Dale Coyne Racing's No. 18 car, led for 47 laps and finished 13 seconds ahead of defending IndyCar champion Ryan Hunter-Reay.
The 29-year-old Briton, who didn't compete at last week's Indianapolis 500, won for the first time since April 2011 when he triumphed on the street circuit in Long Beach, Calif., while driving for Andretti Autosport.
Conway also secured the pole position for Sunday's second race, giving the Dale Coyne team its first pole.
Coyne teammate Justin Wilson finished third Saturday on the 2.36-mile, 13-turn Belle Isle circuit.
Defending Detroit champ Scott Dixon took fourth.
Helio Castroneves grabbed the lead in the IndyCar point standings with a sixth-place run.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys