The last of the big-city political machines was wrecked tonight when Mayor Michael A. Bilandic conceded that he had been defeated in the Democratic mayoral primary by Jane Byrne.

Byrne, 44-year-old protege of the late mayor Richard J. Daley, broke with city hall in 1977, accusing Bilandic of "greasing an unwarranted taxi fare increase."

Bilandic was the political heir to the Daley machine. He was appointed interim mayor at Daley's death, and easily won a special election in 1977 to fill out his term. Chicago, under Daley, had been called the only big U.S. city that works. This winter, it didn't.

With 2,925 out of 3,100 precincts reporting, or 94 percent of the ballots cast, Byrne had 385,263 votes, or 50.7 percent, and Bilandic had 373,337 votes, or 49.2 percent.

The issue that put Byrne over the top was the Bilandic administration's bungling of clearing city streets during this year's record snowfall, which now totals more than 90 inches. With a small and underfunded campaign, Byrne aroused little interest among the electorate until the snow started falling on New Year's Eve.

Thousands of voters who had been apathetic in previous mayoral elections turned out today to put Bilandic, onetime alderman of Daley's ward, out of office. Byrne's victory was seen more as an anti-machine vote than a vote for her personally. In recent weeks, when her momentum began to build, the only issue in the campaign had been the handling of the record snowfall.

Byrne greeted hundreds of enthusiastic supporters in a Near North Side hotel a few minutes before Bilandic conceded. The enthusiastic crowd surged around her, shouting and chanting, "Jane! Jane!"

One of the architects of her campaign, independent organizer Don Rose, stepped to a microphone and shouted, "Hey, people. It would be a hell of a thing to elect a new mayor and then suffocate her," Victory in Chicago's Democratic primary is tantamount to election, with only token GOP opposition.

Byrne was the city's commissioner of consumer sales under Daley, a job that gave her control over the city's taxicabs.

After Bilandic became mayor upon Daley's death, the Chicago City Council approved a controversial fare increase for cabs, which are operated primarily by the Checker Motors Corp. empire.

Byrne charged that a "cabal of evil men" including Bilandic and two regular Democratic organization aldermen pushed the increase through in violation of a city ordinance.

She called the scandal a "Taxigate." The Justice Department investigated her charges and announced recently that it had concluded the investigation without seeking indictments.

Throughout the campaign, she praised the late mayor Daley and accused Bilandic of undermining "the city that works."

The recent blizzard so shook public confidence that Byrne's campaign led to one of the biggest upsets in the city's history.

A stern-looking and tough-talking woman, Byrne was first befriended by the late mayor Daley when she was working for the 1960 election of John F. Kennedy. Daley was a strong supporter of Kennedy, and is widely credited with securing his election with Chicago votes that may have been stolen.

Byrne showed great strength among black voters, carrying several black wards that traditionally have gone to the Democratic machine. The city is now estimated to be nearly 50 percent black.

At the Byrne victory celebration, one young supporter summed up perhaps the feeling of most: "I don't believe this is happening. It's like Dumbo the elephant flying."