Most Republicans described Ms. DeVos as committed to what is best for children. In a fiery speech moments before the vote, Senator Lamar Alexander, Republican of Tennessee and a former education secretary himself, criticized his Democratic colleagues for opposing Ms. DeVos, he said, simply because she was nominated by a Republican president.

“She led the most effective public school reform movement over the last few years,” he said. Mr. Alexander, the chairman of the committee that approved Ms. DeVos’s nomination last week in a party-line split, said she had been “at the forefront” of education overhaul for decades.

By midday Tuesday, as the vote in the Senate deadlocked at 50 to 50, Mr. Pence, a former member of the House, took the gavel and at 12:29 p.m. declared his vote for Ms. DeVos. In a procedural quirk, a confirmation vote on Senator Jeff Sessions of Alabama for attorney general was scheduled after that of Ms. DeVos so he could vote “yes” before leaving the Senate, securing Republicans a decisive vote.

Raised in a wealthy family, Ms. DeVos, who married into the Amway fortune, has a web of financial investments, has also raised alarm among critics who worried about the many opportunities for conflicts of interest. She was the first of Mr. Trump’s nominees not to complete an ethics review before appearing before a Senate panel. She filed her ethics paperwork on Jan. 19, two days after her confirmation hearing.

Teachers’ unions and even some charter organizations had protested Ms. DeVos’s nomination across the country. Senator Patty Murray of Washington, the top Democrat on the committee that approved Ms. DeVos — and a former educator herself — urged disheartened advocates on Tuesday morning before the vote not to think of their efforts as a waste.

“It’s made an impact here and made a difference,” she said. “And I think it’s woken each of us up in this country to what we value and what we want.”