This coming Labor Day weekend, traffic in downtown Baltimore will move at more than 100 miles per hour—or not at all: The city's main streets will be closed so that IndyCar racers can compete in the inaugural Baltimore Grand Prix. Much more than prize money is at stake.

Nine days later, on Sept. 13, voters will pick a mayor, and incumbent Stephanie Rawlings-Blake is betting that the auto race will draw thousands of free-spending tourists and stimulate the local economy, thereby demonstrating her vision and competence. In fact,...