With the support of the Democratic Party machine that she crushed five weeks ago, Jane Byrne was elected mayor of the nation's second largest city today by a record majority.

With 96 percent of the vote tallied, Byrne, a former protege of the late mayor Richard J. Daley who broke with the party machine last year, had crushed Republican investment banker Wallace Johnson by 82 to 16 percent. A third candidate, the Socialist Workers Party's Andrew Pulley, had 2 percent.

It was the largest percentage margin of victory in history for a mayoral candidate here, topping the 77.6 percent that Daley received in 1975, his best showing.

In a victory statement, Byrne promised a "new renaissance for Chicago . . . I hope everyone here will always remember what we started in the winter of '79, and I hope that spirit will never end."

Her husband, Jay McMullen, a reporter with The Chicago Sun-Times, said, "I'm glad my wife finally found work."

Byrne, who urged voters to "make me look big," thus became the first woman mayor of the "the city with broad shoulders." By virtue of her office and margin of victory, she also becomes a major force to be reckoned with in national Democratic Party circles.

Her election, which had been expected since she won the Feb. 27 primary, caps one of the biggest political upsets in this city's history. And it raises questions about the future of the last of the old, big-city political machines, its role in state and national politics, and the direction Chicago, which proclaims itself "the city that works," will take under Byrne.

Byrne, 44, has been skillfully making peace with the machine ever since she upset Mayor Michael A. Bilandic, the machine's candidate, in the primary. And the machine-along with organized labor, big business and almost everyone else here-has been making peace with Byrne, largely because there was no other choice.

Byrne has been tough but conciliatory. "She went into every lion's den in the system and made all the lions look like pussycats," one machine loyalist said.

Today the old ward bosses, the wheelers and dealers who five weeks ago sought to bury Byrne, acted as if they invented her. "Skid Row has ways delivered before, and it is delivering for Jane Byrne," said city sewer boss Ed Quigley, paraphrasing a remark he made several weeks ago.

His logic is instructive, "I'm strictly organization, no matter who is candidate," he said in an interview. "I'm a Democrat. She's a Democrat. And she's going to be boss. The boss is the boss. Things will go on."

What will happen to the Daley machine is a matter of great conjecture here. Republicans, who quietly admit that Johnson's bumbling candidacy was an embarrasment to the party, are licking their chops over what they assume is the machine's carcass.

"There's no question that the Chicago machine was defeated in February. It will never be the same," said state GOP Chairman Don Adams."She was elected by independents, not the machine. The whole party was weakened. Potential for Republican progress has never been better."

But others argue that Byrne's election will revitalize the machine, by bringing in new blood, and leave it stronger than ever. The Carter administration apparently agrees; it has been courting Jane Byrne as if she were a prom queen.

President Carter, who supported Bilandic, called to congratulate Byrne after the primary, Presidential aides Jack Watson and Tim Kraft invited the head of Byrne's transition team, Dr. Louis Masotti, to Washington to brief him on Carter's transition effort in 1976. Last week Byrne was invited to the White House for the Mideast peace treaty signing ceremony. But she skipped the daytime ceremonies in Washington in order to attend a meeting of precinct workers here.

When she showed up at the evening dinner celebrating the treaty, Byrne, who got her start in politics in John F. Kennedy's 1960 presidential campaign, was arm in arm with Sen. Edward M. Kennedy (D-Mass.), a potential Carter rival next year.

Traditionally, Chicago mayors have been among the most powerful voices in the Democratic Party. Byrne will likely carry on that tradition, according to aides.

Twelve other U.S. cities with populations over 100,000 including Cincinnati and San Francisco, have women mayors. None, however, has the clout of Byrne. As a longtime member of the Democratic National Committee, she also knows the territory.

"There's no question that she'll be one of the strongest women voices in big-league politics," says Alderman Roman Pucinski, a former congressman.

Byrne ran in the primary as an independent maverick, harshly critical of city corruption and Bilandic's failure to clear the snow off the streets. She has run since then as a conciliator who can unite the city and redistribute power.

She has given only vague hints about what her administration will hold. Apparently, there will be no wholesale firings, although the police chief and the head of the health department are expect to be dismissed. The city's patronage system is expected to continue.

Her chief priority in position papers appears to be to shift more power and economic development money away from downtown and into neighborhoods. She has said she wants to restructure the school board and put tight controls on converting apartments into condominiums.

"She's a very tough lady, and she intends to use the political power she has assembled," sayss transition chief Masotti, and urban affairs specialist from Northwestern University. "I anticipate change, not drastic, change, not revolutionary change, but directed change."

Who is Byrne's model for this? Richard J. Daley, Masotti answers. CAPTION: Picture, Cook County Democratic Chairman George Dunne applauds Jane Byrne. AP