This article quotes Dr. Larry Sabato, a political scientist at the University of Virginia, as saying that Tom Clements may outpoll Alvin Greene in this year’s U.S. Senate race in South Carolina. Clements is the Green Party nominee and Greene is the Democratic Party nominee.
The only Green Party nominee for U.S. Senate who ever outpolled either the Democratic or the Republican nominee for U.S. Senate in any general election, so far, was Jed Whittaker in Alaska in 1996. He polled 29,037 votes, and his Democratic nominee polled 23,977.
No Libertarian has ever outpolled a major party opponent for U.S. Senate. The closest any Libertarian Party nominee came to doing that was Carla Howell in Massachusetts in 2000. She polled 308,860 votes and her Republican opponent polled 334,341 votes.