Sen. Lindsey O. Graham (R-S.C.) comfortably won his Republican primary Tuesday, defeating a field of six lesser-known challengers who failed to gain any traction against the backdrop of a tea party movement unhappy with the second-term senator.

Graham's win marked the latest round of good news for Republican senators facing reelection in 2014. Many drew conservative primary challengers; but those challengers have mostly fallen flat.

Viewed with skepticism by conservatives over his support for immigration reform, among other things, Graham waged an early and expensive effort to discourage strong challengers and prevent the ones who did run against him from making strides.

With nearly all precincts reporting, Graham had 57 percent of the vote, well ahead of second-place finisher Lee Bright, a state senator, who had 15 percent. The Associated Press called the race about two hours after polls closed. The five other candidates were in single-digits. Graham needed to win more than 50 percent to avoid a top-two runoff in a fortnight.

Like Graham, the two top-ranking Republican senators -- Mitch McConnell (Ky.) and John Cornyn (Tex.) -- each skated past their conservative opponents earlier this year. Republicans challenging Sens. Lamar Alexander (R-Tenn.) and Pat Roberts (R-Kan.)​ haven't picked up much momentum ahead of primaries set for later this summer.

The tea party's best hope to dislodge a Senate Republican will come in Mississippi on June 24. There, Sen. Thad Cochran (R) was forced into a runoff by state Sen. Chris McDaniel (R), who won more votes in last week's primary. National tea party groups have spent millions of dollars helping McDaniel.

But those groups, which eyed Graham at the outset of the election cycle, mostly steered clear of South Carolina, where none of Graham's opponents caught fire. Graham's early preparation, robust fundraising and heavy spending kept top opponents from challenging him and lower-tier challengers from moving up in the polls. Graham spent more than $7 million through late May, according to campaign finance records.

First elected to the Senate in 2002, Graham will be a substantial favorite to win a third term in November against state Sen. Brad Hutto, the Democratic nominee. South Carolina leans heavily to the right.

South Carolina was one of six states where voters went to the polls in runoffs and primaries Tuesday. Maine, Nevada, North Dakota, Virginia and Arkansas also held elections.

In the competitive district being vacated by Rep. Mike Michaud (D-Maine), who is running for governor, state Sen. Emily Cain defeated fellow state Sen. Troy Jackson in the Democratic primary by a wide margin. Former state treasurer and gubernatorial candidate Bruce Poliquin won the Republican race and will face Cain.

Updated at 11:24 p.m.