WASHINGTON — In an election year shaped by voter anger toward the political establishment, the outcome of an unusually large number of close Senate and governor’s races could be determined by the outsize role of third-party candidates.

The potential spoilers include a quixotic former three-term senator, a pizza delivery man and an Alaskan whose name, Fish, summons a favored native food. They represent independents, Libertarians and other parties that have suddenly become relevant — and could affect the balance of power in Congress and decide who runs the governor’s offices in several states.

“If people don’t like their choices with the Republican candidate or the Democratic candidate, then you’re going to see a spurt in third-party candidates, so they can definitely affect outcomes,” said Senator John Cornyn, Republican of Texas.

To mitigate the impact of Libertarian candidates in North Carolina and other states, Republicans are enlisting Senator Rand Paul of Kentucky to appeal to Libertarian-leaning voters. The U.S. Chamber of Commerce last week recorded commercials featuring Mr. Paul, which will air in closely contested states.