Gov. David Pryor and first-term Rep. Jim Guy Tucker emerged on top of a tight primary race for the Democratic State nomination in Arkansas yesterday, setting the stage for a June 13 runoff that should be a cliffhanger.

Unofficial final returns showed that Pryor led in Tuesday's primary with 34.5 percent of the vote and that Tucker squeaked past his colleague, Rep. Bay Thornton, 32.5 percent to 32 percent. Political novice A. C. Grigson had 1 percent.

Most political professionals in Arkansas, including pryor, had expected the governor to win a larger portion of the vote. He was the the best-known of the three major contenders when the campaign began, and had come close to defeating the late Sen. John L. McClellan in the 1972 primary.

But Tucker and Thornton campaigned harder and spent more money than did Pryor. Tucker was particularly helped by endorsements, and contributions, from most labor organizations, including the AFL-CIO and teachers' unions.

The winner of the Tucker-Pryor runoff will be an overwhelming favorite in November to defeat Republican Tom Kelly, a liberal who suggests a national economic policy based on E. F. Schumaker's book, "Small is Beautiful."

From the labor standpoint, the upcoming runoff presents a replay of 1972 - with an inside twist. Then, too, labor support helped a young congressman win a spot in a runoff. But that year the congressman with labor's backing was Pryor; McClellan, the incumbent senator, beat back the challenge by making a big issue of Pryor's alliance with the unions.

This year Pryor is anathema to union leaders because on his use of National Guard troops to break a fire-fighters' strike and his outspoken opposition to the labor revision bill before the Senate. Tucker is a strong backer of the labor bill.

A senior Arkansas Democrat, who asked to remain anonymous "in case my guess turns out to be wrong," postulated yesterday that labor backing might not help Tucker particularly in the runoff.

The winner will be the candidate who can lure most of the vote that went to Thornton Tuesday. Thornton ran strongest in rural areas, where labor endorsements are not generally helpful.

Traditional political analysis would suggest that Pryor, generally described as a "moderate," would hold more appeal for rural voters than would Tucker, whose major backing has come from urban professionals and union members.

But another Arkansas political tradition suggests that the candidate who runs second in a lose primary - as Tucker did Tuesday - is likely to win the run off. Playing one tradition against another, the June 13 election looms as a tossup.

Tucker can take heart from the surprising result of Tuesday's Democratic primary runoff for the Senate in North Carolina. There, state Insurance Commissioner John Ingram upset Luther Hodges Jr., the consensus choice of the state's Democratic and business establishment, to win the right to challenge incumbent Jesse A. Helms (R) in November.

Hodges spent nearly $1 million on the primary, Ingram one-twentieth as much.Hodges carried 85 of the states 100 counties in the May 2 primary, Ingram fewer than 10.

But in their runoff Ingram convinced the voters that he was the little man's friend by constant reiteration of his battles against insurance rate increases.

With the momentum from his upset victory and organizational and financial support from the Democratic Party, Ingram could pose a stiff challenge to Helms.

Following is a list of winning congressional candidates in Arkansas. Incumbents are indicated with an (I); candidates without opposition are indicated with an X.