COLUMBIA, Mo. — When the first $150,000 check showed up in his campaign account, Shane Schoeller was locked in a tight Republican primary for the unheralded office of Missouri secretary of state, battling two fellow lawmakers with virtually identical platforms.

An additional $250,000 arrived in August, after Mr. Schoeller had nearly run out of money and faced a tough general election campaign against a well-financed Democratic opponent.

Mr. Schoeller’s angel is a retired investor and chess enthusiast named Rex Sinquefield, who in recent years has emerged as the biggest political donor in Missouri and one of the most prolific anywhere in the country.

Since 2008, when Missouri abolished contribution limits, Mr. Sinquefield has donated more than $20 million to local candidates and political action committees, driving the political debate on issues like education, upending the political world here and making him perhaps the most influential private citizen in the state. More than half of that money has gone to advance his signature cause: eliminating state and local income taxes in Missouri, a major source of government revenue, and replacing them with sales taxes.