Alabama Attorney General Charles Graddick, a conservative who promised to make Alabama "the comeback state," narrowly defeated Lt. Gov. Bill Baxley last night in the battle to determine who will succeed Gov. George C. Wallace and begin a new political era.

With all but 36 of 4,230 precincts reporting unofficial returns, Graddick had 460,357 votes and Baxley 450,507 in the Democratic gubernatorial runoff.

Graddick, declaring he had "God on my side," claimed victory. "Blood, sweat, tears and money have paid off," he told a victory celebration in Montgomery.

Baxley refused to concede. He told supporters that, if the count holds up, he would "pledge my support to him and the entire ticket."

The official canvass will not be completed for several days.

Baxley had jumped to an early lead with returns from labor strongholds outside of Birmingham and ran strong in the state's Black Belt. Graddick carried his populous hometown of Mobile by 2 to 1 and picked up strength in other urban areas.

Baxley, a populist trying to hold together a shaky coalition of blacks and rural whites, easily won the June 3 primary with the support of teachers, labor unions and the state's two premier black political organizations. But Graddick, backed by big business interests, severely damaged Baxley's popularity by attacking his "moral character" and ties to "special interests." He is only the third politician in this century to come from a second-place spot in a primary election to win an Alabama gubernatorial runoff election.

The results could have major repercussions on southern politics. Democrats in the region have controlled state offices since the early 1970s by maintaining a coalition of blacks and whites. While Baxley, a liberal, courted black support, Graddick ignored blacks and was accused of promoting racial division. He was endorsed by the Ku Klux Klan, but disavowed the endorsement.

Graddick will be a strong favorite next fall against Republican Guy Hunt, who is given little chance of becoming Alabama's first Republican governor since Reconstruction.

Jim Folsom Jr., son of the legendary 6-foot-8 former governor, James E. (Big Jim) Folsom, defeated state Sen. John Teague to win the Democratic nomination for lieutenant governor.

George Wallace Jr., son of the four-term governor, narrowly defeated Jim (Watchdog) Zeigler in the Democratic runoff for state treasurer.

The election was held amid a dispute over who could vote. Alabama voters do not register by party, and Republicans traditionally cross over to vote in the Democratic runoff.

But one judge, acting on a request by state Democratic officials, issued a restraining order Monday saying that the 35,000 people who voted in the June 3 Republican primary could not vote in yesterday's runoff.

Three hours later a Mobile judge ruled that Republicans could vote. Graddick, needing GOP votes to win yesterday's runoff, issued an attorney general's opinion saying it was legal for Republicans to vote. A series of confrontations at the polls resulted.

When Gov. Wallace, a paraplegic, announced tearfully in April that he would not seek a fifth term, many Alabamians hoped it would usher in an era of politics that would improve the state's image.

Instead, the Baxley-Graddick contest turned into a carnival of name calling and sexual innuendo. Graddick, 41, called Baxley a "liar" for not telling the truth about the alleged use of a state car to ferry a young woman to his apartment. Baxley, 45, called Graddick a "coward" for backing out of a debate. Graddick suggested a fist fight to settle everything.

In Alabama's only congressional runoff, Claude Harris, a former circuit judge from Tuscaloosa, defeated District Attorney Billy Hill of Montevallo, for nomination to the seat held by Rep. Richard C. Shelby (D-Ala.), who is running for the Senate. The winner is expected to face tough opposition from GOP nominee Bill McFarland.

Two congressional runoffs were held in South Carolina.

In the 1st district, former representative Mendel Davis, a 10-year-veteran who retired in 1980, was defeated in a comeback bid by James Stuckey, a Charleston County councilman, in the Democratic runoff. Stuckey will face GOP state Sen. Arthur Ravenel.

In the 4th district, Greenville Mayor Bill Workman (R) easily defeated airline pilot Ted Adams (R). Workman will face state Sen. Elizabeth Patterson, daughter of the late senator Olin Johnson (D-S.C.).