Mississippi did something yesterday it hasn't done since Reconstruction. In a race fragmented by a black civil rights leader, it decided to send a Republican to the U.S. Senate.

Rep. Thad Cochran, a Jackson attorney, benefited as black votes were drawn away from his Democratic opponent by independent candidate Charles Evers, the mayor of Fayette. Cochran jumped to an early lead in the race to win the seat Sen. James O. Eastland (D-Miss.) has held since the 1940s. He was projected winner by CBS and ABC News.

In Tennessee, NBC and CBS news projected that Republican Lamar Alexander, a former Nixon White House aide, would defeat banker Jake Butcher in one of the most expensive campaigns in the nation's history.

Senate Majority Leader Howard Baker (R-Tenn.), Sen. Jesse Helms (R-N.C.) and Sen. Strom Thurmond (R-S.C.) also appeared to be victors in their respective states, according to network projects.

But further hopes of Republican in-roads appeared to be falling by the side in the South.

Particularly noteworthy were early leads taken by Democratic gubernatorial candidates in both Florida and South Carolina.

Robert Graham, a state senator, appeared to be on his way to defeating Jack M. Eckerd, a multimillionaire drug chain owner, in Florida's free spending governor's race, according to network projections. And President Carter's 1976 South Carolina campaign manager, former state senator Richard W. Riley, appeared to be easily winning the governorship in that state.

Democrats were also holding onto Senate seats in Kentucky, Georgia, Arkansas, Alabama, and Louisiana.

Meanwhile, Democrats appeared to be on the verge of picking up the Senate seat now held by Republican Sen. Dewey Bartlett. CBS and ABC news projected Oklahoma Gov. David Boren the winner there over Robert B. Kamm, the former president of Oklahoma State University. Alabama

In a watershed year in Alabama politics, Democrat Forrest (Fob) James, who faced only minor Republican oppositions, was projected by NBC as the winner in the race to succeed Gov. George Wallace, who has dominated state politics for two decades. James, a barbell manufacturer who until two years ago was a leading Republican fund-raiser, ran as a successful businessman who would bring "a renaissance of common sense" to the state.

Democrat Howell Heflin, the state's former chief justice, had no Republican opposition.He will succeed retiring Sen. John Sparkman, chairman of the Senate Foreign Relations Committee.

Donald Stewart, a liberal state senator, moved into an early lead in the state's other hotly contested U.S. Senate race and was projected a winner by ABC News. His GOP opponent, former congressman James D. Martin received more than $230,000 from the Republican National Committee, to give his late-starting campaign a boost. Arkansas

Gov. David Pryor (D) was leading Republican Thomas Kelly for the Senate seat held by John L. McClellan (D) before his death, and the governor's office appeared likely to stay in Democratic hands.

As expected, State Attorney General Bill Clinton (D) was running far ahead of GOP State Chairman A. Lynn Lowe for the governorship. Clinton, 32, would be the youngest governor since Harold Stassen was elected at 31 in 1938.

ABC projected both Pryor and Clinton as winners.

McClellan's Senate seat is now held by Kaneaster Hodges Jr., who was ineligible to run under the state consitution. Florida

In a battle of multimillionaires, Robert Graham, an obscure state senator who worked a 100 different jobs to attract attention, jumped to an early lead in the Florida's governor's race. ABC News projected he could collect 57 percent of the vote and succeed popular Gov. Reubin Askew.

Graham's free-spending opponent, Jack M. Eckerd, the owner of a drug store chain, was unable to disassociate himself from scandals in the General Services Administration, which he directed during the Ford administration. Georgia

Democrats Gov. George Busbee and Sen. Sam Nunn held commanding leads over their Republican challengers, GOP State Chairman Rodney M. Cook and former U.S. attorney John Stokes, respectively.

Both Busbee and Nunn are popular incumbents and had been expected to win reelection easily. Kentucky

Sen. Walter (Dee) Huddleston, a Democrat, won an easy victory over GOP state representative Louie Guenthner, in sharp contrast to his narrow first-term victory six years ago.

Huddleston, with Democrats united behind him, began the campaign so strong that more prominent Republicans were scared off. Guenthner tried to tag Huddleston as the most liberal senator from the South and hammered away at his vote for the Panama Canal treaties, to no avail. At one point, Guenthner even complained that he was being ignored by the state Republican Party.

In a hotly contested race for a House seat that has been in Democratic hands for 50 years, Republican Larry Hopkins defeated Democrat Tom Easterly, who had ousted Rep. John Breckinridge in a primary last spring. Mississippi

Mississippi appeared on the verge of sending its first popularly elected Republican senator to Washington in history last night. With only early returns in, CBS and ABC news declared that voters would select Rep. Thad Cochran, a Jackson attorney, to succeed Sen. James Eastland who is retiring, in a fiercely contested, three-way race.

Charles Evers, the brother of slain civil rights leader Medgar Evers and a folk hero among many blacks, was drawing a heavy black vote, and his independent candidacy appeared to be drawing votes away from Democrat Maurice Dantin, for whom Eastland had campaigned. North Carolina

Republican Sen. Jesse Helms, who became known as the "Six Million Dollar Man" for his expensive reelection campaign, was leading Democrat John Ingram in early returns. ABC and CBS projected Helms as the winner. Oklahoma

Democratic Gov. David L. Boren held an early lead over Republican Robert B. Kamm, a former president of Oklahoma State University, in their campaign for the seat of retiring Sen. Dewey F. Bartlett (R). ABC and CBS projected Boren as the winner.

Both are conservatives who favored deregulation of oil and natural gas in this energy-rich state. Both also supported the Kemp-Roth tax-cutting bill. Kamm was more heavily financed than Boren and got an assist from former president Ford. Boren is concluding his first term as governor. South Carolina

Sen. Strom Thurmond (R-S.C), who campaigned as "more than just a senator," openly courting the black vote after a lifetime as one of the nation's most prominent segregationists, easily defeated Democratic challenger Charles D. (Pug) Ravenel.

Six years ago Ravenel, a South Carolina-born investment banker who spent seven years on Wall Street, burst onto the South Carolina political scene, winning the Democratic gubernatorial nomination only to have the courts decide he didn't meet the state's residency requirement.

Thurmond tagged him a "carpetbagger" who supported the Panama Canal treaties, labor law revision and other liberal positions, and Ravenel had trouble finding an issue to hang around his 75-year-old opponent's neck.

In the race for governor, former state senator Richard W. Riley (D), who was President Carter's 1976 campaign manager for the state, was the projected winner, according to CBS and ABC, over ex-Rep. Edward L. Young (R) to succeed retiring Gov. James B. Edwards (R).

Riley had a reputation as a reformer who had healed the severe Democratic Party division that led to Edward's election as the first Republican governor since Reconstruction four years ago. Tennessee

Former Nixon White House aide Lamar Alexander was running well ahead of Democrat Jake Butcher (D) in a hard-fought race to succeed retiring Gov. Ray Blanton, while Senate Minority Leader Howard H. Baker (R) led Democrat Jane Eskind in his bid for a third term.

According to NBC and CBS those two networks also projected Alexander as the winner.

Butcher, a wealthy banker and friend of Bert Lance, had an edge over Alexander in spending and party registration, but Alexander was an aggressive campaigner, criticizing Butcher's failure to make a financial disclosure and his high-rolling banking practices.

The Baker-Eskind campaign was marked by controversy over Baker's national ambitions and his support of the Panama Canal treaties. Virginia

Former attorney general Andrew P. Miller (D) held a narrow early lead over Republican John W. Warner, a former secretary of the Navy, in their race to succeed retiring Sen. William L. Scott (R). Miller was bucking a recent GOP trend in this once staunchly Democratic state