More than two-thirds of the Democrats’ cash went to a dozen presidential battlegrounds critical to any Clinton victory. The biggest beneficiaries were Florida, which has taken in close to $3.5 million, and Pennsylvania and Ohio, which have each received more than $2 million.

In each of those states, the funds from the national party have made a difference, erasing deficits in federal contributions against the respective Republican state parties.

The money followed a legal but circuitous route turbocharged by the 2014 ruling in McCutcheon v. Federal Election Commission, which struck down Watergate-era limits on the combined amount one person could donate to all federal candidates and parties in an election cycle.

Like other candidates for federal office this year, Mrs. Clinton can accept only up to $5,400 from any one donor over the course of her campaign. But after the McCutcheon decision, Mrs. Clinton established an agreement last year with the Democratic Party under which she asked her wealthiest patrons to write checks in excess of $300,000, more than double the old limit, to the Hillary Victory Fund, an account made up of the national and state parties and the Clinton campaign.

That amount is a lump sum equal to the total contributions each donor is allowed to give to her campaign and the Democratic National Committee, along with $10,000 to each of the 38 state party organizations now participating in the arrangements.

Because there are no limits on how much money party committees can transfer to one another, most of the state parties have cycled their share back to the Democratic National Committee. The party then moved the cash into a smaller number of battleground states to prepare for Election Day.