CHICAGO — The race for Illinois governor has come down to this: the multimillionaire versus the billionaire.

Gov. Bruce Rauner, a private-equity executive seeking a second term in office, prevailed in a tough battle for the Republican nomination on Tuesday, while J.B. Pritzker, a billionaire philanthropist and venture capitalist from a prominent Chicago family, won the Democratic nomination for governor, according to the Associated Press.

Their victories promise a contest that will be fiercely fought and dominated by big money, with each candidate controlling tremendous sums of personal wealth to spend on his campaign. The two men have already raised more than $150 million, on track to become one of the most expensive governor’s races in history.

In the state’s most closely watched congressional primary, the longtime Chicago-area Representative Daniel Lipinski narrowly defeated a challenger from the left, Marie Newman, according to the A.P. The race became something of a proxy between moderate and progressive Democrats.