Representative Elissa Slotkin, a Democrat with a strong national security background, has defeated former Representative Mike Rogers in the race for Michigan’s open Senate seat, according to The Associated Press.

Her victory keeps the seat in Democratic hands, preventing Republicans from further expanding their new majority. Senator Debbie Stabenow’s retirement at the end of the current Congress set up the competitive race in the key swing state of Michigan.

The contest was one of the last Senate races to be called, and Mr. Rogers had appeared to have the lead until Wednesday morning, when Ms. Slotkin began to inch ahead.

The contest seemed evenly matched. Mr. Rogers and Ms. Slotkin had represented the same swing region of Central Michigan, in and around Lansing. Both came with national security credentials, he from his time at the F.B.I. and leading the House Intelligence Committee, she from the C.I.A. and national security posts in the White Houses of George W. Bush and Barack Obama.

Ms. Slotkin, 48 and a three-term lawmaker, led in the polls for much of the contest. She was the latest Democratic woman in Michigan to make a statewide impression after women there captured the governor’s mansion, the attorney general’s post and the office of secretary of state. With Ms. Stabenow, who has held the seat since 2001, a constant companion on the campaign trail, Ms. Slotkin emphasized abortion rights to her advantage.

But as the presidential race tightened in Michigan, so did the Senate race.

On Wednesday, Ms. Slotkin said she was prepared to work with Republicans in Washington, and acknowledged that some voters had supported both her and President-elect Donald J. Trump.

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