The Frenchman took inspiration from Alexander Rossi's stunning victory at last week's Indianapolis 500 by using a smart strategy at Belle Isle Park.
KV Racing Technology's Bourdais started from 13th on the grid but outsmarted the leading pack in the pits, emerging from his final stop with 13 laps to go in first place.
"The car was obviously really quick. All we needed was clean air to come back from that pretty average qualifying," Bourdais told ESPN after the race.
"I couldn't dream of that, I don't know how we got there. Couldn't be any happier today.
"I think [the strategy] would have worked even better had we not pitted with everyone else. For a long time I really thought the strategy was a total mess and wasn't going to work."
The former Formula One Toro Rosso driver held off a late charge from Dale Coyne Racing's Conor Daly, who claimed his first podium in IndyCar after finishing 2.0401seconds behind Bourdais.
Team Penske's Juan Pablo Montoya completed the podium, with Graham Rahal and Helio Castroneves rounding out the top five in Detroit.
Despite his 13th-place finish, Simon Pagenaud managed to extend his IndyCar Series lead after Penske team-mate Scott Dixon finished 19th due to a mechanical problem.