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Hillary Clinton raised substantially less for her presidential campaign in January than her Democratic rival, Senator Bernie Sanders of Vermont, according to an unofficial tally Mrs. Clinton released on Thursday. The totals provide something of a psychological, as well as a financial, boost for Mr. Sanders and his supporters as he seeks to defeat Mrs. Clinton in the New Hampshire primary on Tuesday.

Mrs. Clinton raised $15 million in January, while Mr. Sanders raised $20 million. Mrs. Clinton also raised another $5 million in joint efforts with the Democratic National Committee. But while that money will aid Mrs. Clinton if she becomes the nominee, it is unavailable to her during the nominating battle.

While full details will not be available until both candidates file quarterly fund-raising reports with the Federal Election Commission in April, the advantage for Mr. Sanders underscores how the fiery liberal senator has rewritten the rules of large-scale presidential fund-raising. Virtually all of his cash has come from grass-roots donors giving less than $200, whereas Mrs. Clinton has assembled a more traditional fund-raising operation that relies more heavily on wealthy “bundlers” and donors giving the maximum of $2,700.

Mr. Sanders has now raised more money in total than any candidate except Mrs. Clinton herself. (Mrs. Clinton reported substantially more cash on hand than Mr. Sanders at the end of December.)