Bernie Sanders proved his grit in the Democratic presidential race on Tuesday, defeating Hillary Clinton in Michigan and showing strength for the first time in a large, racially diverse state far from his home base of New England.

Mrs. Clinton easily captured Mississippi, completing a clean sweep of the Deep South powered by her overwhelming popularity among African-American voters in the region. But Mr. Sanders, in winning his most populous state this primary season, made inroads with black voters in Michigan, according to exit polls, winning 30% of the state’s African-American primary vote.

With 92% of precincts counted in Michigan, Mr. Sanders had 50% of the vote to 48% for Mrs. Clinton. The state will award, proportionally, 130 pledged delegates to the summer Democratic convention.

The win gives Mr. Sanders a jolt of momentum at an important moment in the race. He and Mrs. Clinton face off Wednesday in a debate in Florida. Nearly 700 convention delegates are at stake in the next round of voting, next Tuesday, and the Sanders camp hopes the Michigan result will reverberate in two other large Midwestern states that vote then: Ohio and Illinois.

The other three states to vote next Tuesday are Florida, Missouri and North Carolina.