Democratic Party leaders yesterday elected Paul G. Kirk Jr., a former aide to Sen. Edward M. Kennedy (D-Mass.), as new party chairman, then derailed Mayor Richard G. Hatcher of Gary, Ind., the chairman of the Rev. Jesse L. Jackson's presidential campaign, as party vice chairman.

The elections highlighted a day of deal-making and name-calling that left Democrats divided along regional and racial lines and produced bitterness among the losers who expressed resentment over the power demonstrated by organized labor during the three-day meeting of the Democratic National Committee.

The divisions signaled a continuing free-for-all in the months ahead over the party's direction as it seeks to recover from President Reagan's landslide reelection victory.

Angry black caucus leaders denounced the election of Illinois comptroller Roland Burris, also black, as party vice chairman after their caucus had voted in favor of Hatcher. They accused Kirk of ignoring the sanctity of the caucus recommendation and labeled Burris an "Uncle Tom" for refusing to accept the caucus' decision to support Hatcher.

Similarly, many southern Democrats left town complaining that the national party had done nothing this week to appeal to moderate-conservative voters in their region and vowed to go their own way.

"We don't need their help and we don't need their interference, and we don't need them slopping things over on us," said Texas Democratic Chairman Bob Slagle of the national party organization. "I doubt seriously that people in Texas will think electing a Kennedy chief of staff as party chairman is a moderate signal."

Kirk, 47, fended off a final challenge yesterday after one of his leading opponents, Nancy Pelosi, former California Democratic chairman, quit the race and threw her support to former North Carolina governor Terry Sanford. A fourth candidate, veteran Washington political operative Robert J. Keefe, also pulled out just before the meeting began yesterday.

Pelosi, who struck a deal with Sanford early Friday morning, told her fellow Democrats she decided to drop out because "many of you did not think the right message would go out if a woman was elected chairman."

Pelosi said she believed that she could more easily transfer her support to Sanford than he could transfer his support to her because of the resistance to a female chairman at a time when many Democrats said the party must reach out to white males. Sanford, who entered the race in the late stages, agreed to make her finance chairman if he were elected.

That set up a head-to-head contest between Kirk, who was strongly backed by organized labor and the party's liberal wing, and Sanford, who had the vigorous support of southern state chairmen, the backing of Pelosi forces in California and New York, and the endorsements of several prominent Democratic governors, including Arizona's Bruce Babbitt, Virginia's Charles T. Robb, South Carolina's Richard W. Riley and New York's Mario M. Cuomo, who had been a vigorous advocate of Pelosi.

Kirk easily prevailed 203.07 to 150.93. A group of 25 at-large delegates, whose right to vote was the focus of a dispute during the first two days of the DNC meeting, backed Kirk 20 to 5.

Kirk then moved quickly to consolidate his power, forcing one candidate for national finance chairman, Duane B. Garrett, to withdraw, persuading a candidate for party treasurer, William Crotty, to drop his bid, and successfully rallying the party to elect Sharon Pratt Dixon, a DNC member from the District of Columbia, as new party treasurer.

But the swiftness of his actions left his opponents disillusioned, especially southerners who have felt estranged for many months since Reagan trounced Walter F. Mondale and Geraldine A. Ferraro last November.

"He's got to demonstrate some independence," said Alabama Democratic chairman Jimmy Knight. "He's got to demonstrate he's his own man" and not tied to anyone. "I'm talking specifically about Sen. Kennedy."

Kirk pledged to reach out, to listen and learn from the success of local and state Democratic officials in the South and West.

"They have not really had the national party as an asset," he said. "We have to bring those folks to the table of national politics."

Kirk got his way on most of the elections yesterday, but he opened a rift with black leaders by letting the full DNC vote on the disputed vice chairmanship between Hatcher and Burris. Late Thursday, black caucus members voted 32 to 25 to endorse Hatcher and urged that the vote be bindiNg on the national committee. But Burris refused to step aside, and Kirk refused to make him do so. Burris defeated Hatcher 198.27 to 148.72.

In the race for the two other vice chairmanships, Lynn Cutler of Iowa and Colorado state Sen. Polly Baca were reelected, defeating Kentucky State Superintendent of Public Instruction Alice C. McDonald, who won the friendship if not the votes of fellow Democrats by passing out personalized bottles of Kentucky bourbon during the meeting.

Hatcher called his defeat "the end of the effectiveness" of the black and Hispanic caucuses, but denied that it was a vote against Jackson, who had supported his reelection. "You did not in any way do violence to Jesse Jackson or to those who support him," he said.

Burris, in a news conference, said, "I believe in the black caucus and I will work to strengthen the black caucus," adding that many blacks had urged him to carry the fight to the floor yesterday.

Rep. Mickey Leland (D-Tex.), chairman of the Congressional Black Caucus, denounced Burris by comparing him to blacks who had been used by whites during the time of slavery. "The classic term is Uncle Tom," he said.

He said blacks would now have to consider their political options within the party and warned, "Mr. Kirk and all the leadership of the Democratic Party are going to have to answer to us one way or another."