The presidential race began to shift in earnest to the industrial Midwest on Friday, with pivotal contests looming in Michigan, Ohio and Illinois, and Donald J. Trump and Hillary Clinton crossing each other’s paths in a preview of what the general election could hold.

The region is one where Mrs. Clinton performed quite well in the Democratic primaries in 2008, beating Barack Obama in Ohio, Indiana and Pennsylvania (Mr. Obama did not compete in Michigan.) And when she visits a manufacturing center in Detroit on Friday, she plans to reveal a job-creation and wage-growth program, according to her campaign.

But the region — especially Michigan, which holds its primary on Tuesday — has been more welcoming to Republicans lately as its manufacturing-based economy has suffered.

Mr. Trump, with his pointed messages about punishing American companies that send jobs overseas and taking an aggressive stance against countries like China that devalue their currency, is also finding an audience. The New York businessman holds a 10-point lead over his closest competitors in Michigan’s Republican primary, according to a poll released this week by The Detroit Free Press.