Conway was the surprise winner of a race that took a dramatic turn when leader Ryan Hunter-Reay triggered a seven-car accident 24 laps from the finish.
Hunter-Reay had dominated but was chasing Josef Newgarden after Newgarden exited pit road ahead of Hunter-Reay and James Hinchcliffe. Hunter-Reay tried to make an aggressive pass in the fourth turn and instead hit Newgarden.
The accident wiped out Hunter-Reay, Hinchcliffe and Newgarden, damaged Helio Castroneves' car, then collected Takuma Sato, Tony Kanaan and Jack Hawksworth.
It opened the door for Dixon to win, but he conceded to Conway when he had to stop for fuel.