The shifting political tides in a coastal South Carolina congressional district are vividly apparent from the first look at last-minute big donations to Mark Sanford and Elizabeth Colbert Busch, rival candidates for the House seat left vacant when Republican Tim Scott was promoted to the U.S. Senate earlier this year.

Under federal law, any donations of $1,000 or more made during the final days before the May 7 election must be reported to the Federal Election Commission. Over the weekend, both campaigns filed their first reports, and they showed the late money breaking strongly in favor of Democrat ...