The shootout was necessitated when an accident involving Alex Tagliani brought out the caution flags. Shortly after the restart, Dixon got past Bourdais and finished 1.7 seconds ahead of him for his second IndyCar victory in six days.
Dixon also won Sunday's event Pocono Raceway -- his first victory of the season.
Dixon's triumph also came hours after he won the pole position for Sunday's competition.
Bourdais' second-place finish was his first at an IndyCar-sanctioned event.