The minority party led by Joshua Nkomo in the Zimbabwe government won a landslide victory in municipal elections in its Bulawayo stronghold yesterday, demonstrating that tribalism is still a strong force in Zimbabwe's politics.

It was the first time that Nkomo's Patriotic Front party won a major election. Prime Minister Robert Mugabe's party has dominated politics since it swept to power in independence elections in February 1980.

The election, postponed twice because of clashes between Mugabe's and Nkomo's supporters in the southwestern city of Bulawayo, went off without a hitch, according to polling officials. There were few charges of vote fraud and no reports of violence.

The peaceful weekend election is evidence that passions here have cooled since heavy tribal fighting in February around Bulawayo killed about 300 persons and led to fears that the newly independent nation might become embroiled in a civil war.

Mugabe used elements of the white-led former Rhodesian military forces, which fought the guerrillas during the war for independence, to put down the February uprising.

Since then there have been only scattered incidents, the former guerrillas have been disarmed and the two parties have tried to control their verbal attacks on each other.

The victory of Nkomo's party demonstrates that he still holds sway in the heartland of his Ndebele tribe, which comprises about 18 percent of the southern African country's 7 million population. The Ndebeles are centered in the southwest while the majority Shonas, the basis of Mugabe's support, dominate the rest of the country.

The Patriotic Front won all 15 seats on the Bulawayo city council in the black wards. They will join eight whites previously elected to give Zimbabwe's second largest city its first black municipal government.

None of the ward elections in Bulawayo were close with the Patriotic Front winning by margins ranging from 5-to-1 to 20-to-1 over opposition from Mugabe's party and independents.

The demonstration of strength by Nkomo's party is likely to cause Mugabe to go slow, for a while at least, in efforts to bring about a one-party state lest he divide the country along tribal and geographical lines.

Mugabe has said a one-party state, favored in much of Africa, would come about only if it is the "will of the people." Last week Nkomo praised the one-party concept but said it must be based on unanimous agreement.

Nkomo and Mugabe joined forces in the seven-year guerrilla war that ended white rule. It was always a tenuous alliance, however, and they went their separate ways in last year's national elections.

Nkomo's party has four of the 23 Cabinet ministries but many of his followers feel Mugabe has treated him shabbily, especially when Mugabe demoted Nkomo to minister-without-portfolio.

Since then, however, Nkomo has stumped the Ndebele area appealing for calm and influencing his guerrillas to give up their weapons while awaiting induction into the new national Army.

It is widely conceded that Nkomo, appealing to his people in averting a tribal breakup of Zimbabwe.