Rep. Harold Washington (D-Ill.) won election as the first black mayor of Chicago Tuesday, defeating Republican Bernard E. Epton in a strong finish to a bitter, hard-fought campaign that attracted national attention and an estimated record 88 percent turnout of the city's eligible voters.

With the votes in 2,793 of Chicago's 2,914 precincts counted early today, Washington had 636,136 votes or 51.5 percent to Epton's 595,694 or 48.2 percent and 3,590 votes for Socialist Ed Warren. Washington finished strong in the late count after trailing Epton most of the evening.

In his victory speech before a vast crowd that greeted him with a 15-minute ovation about 1:15 this morning local time, Washington said, "We've fought the good fight with unseasoned weapons and a phalanx of people who have never been involved before in a political campaign. This was truly a pilgrimage."

He promised that his administration would include "more people and more kinds of people than any government in the history of Chicago."

Reaching for a broad reconciliation, he said, "The whole nation is watching as Chicago sends a profound message out of the crucible of this city's most trying election. Blacks, whites, Hispanics, Jews, gentiles, Protestants and Catholics . . .have joined together in a new coalition."

Earlier, Epton left his Palmer House Hotel election night headquarters without publicly conceding defeat before his massed supporters. But in a brief, bitter interview with a reporter from station WMAQ-TV, the NBC affiliate, just before he headed home, Epton said he had to "face facts."

Talking in a rambling, exhausted voice, Epton said:

"I certainly hope the city will prosper under the new mayor. I wish Harold luck . . . he'll certainly need all the good help and talent he can get. His expertise in the area of finances certainly leaves a lot to be desired. But maybe he'll learn to pay bills promptly and certainly pay his taxes promptly.

"The black friends that I've lost, perhaps it's just as well that I found out at this stage . . . but certainly in the future, I'll save a lot of money in charitable causes."

Washington, a two-term Democratic congressman who will be 61 Friday, has rewritten the political, racial and social history of this 150-year-old city in the five months since he announced his candidacy for mayor.

He began as an implausible underdog whose political base seemed limited to his 1st Congressional District in the city's South side.

But he put together a grass-roots volunteer campaign that first rolled out a massive black voter registration drive last autumn and then defeated the heavily financed campaigns of incumbent Mayor Jane M. Byrne and Cook County State's Attorney Richard M. Daley for the Democratic nomination in the Feb. 22 primary.

In the general election campaign against Epton, Washington concentrated on raising the black turnout to new records and holding down Epton's strength in the lakefront and Hispanic wards while conceding heavy losses in the ethnic wards on the northwest and southwest sides.

Washington told ABC-TV's Nightline that he expected to win with 53 to 55 percent of the vote and would "reach out" to whites who rejected his candidacy.

"My whole life, I've played coalition politics," Washington said, "and I will be doing that starting tomorrow Wednesday morning" at a "unity prayer breakfast."

The election appeared to be a replay of the primary, when the television stations projected Washington as the winner by a narrow margin while the early, unofficial vote tally showed him trailing. Then, Washington wound up winning by 30,000 votes over Mayor Byrne who refused to concede defeat until the following day.

Washington apparently got more than 90 percent of a huge black vote and was holding Epton to a marginal plurality in the seven crucial lake-front wards. However, Epton ran well in the white ethnic wards in the southwest and northwest.

Washington watched the early election returns at his campaign headquarters in the Loop financial district, then moved on to the massive election-night celebration at Donnelley Hall, a huge downtown exhibition center. Blacks by the thousands thronged the hall.

Epton watched the White Sox home opener today with Republican Gov. James R. Thompson and scheduled his election party at the Palmer House.

Hispanic voters also were turning out in record numbers, Democratic Party officials reported. The 93,000 Hispanic voters were targeted by both Washington and Epton. Their traditional preference has been for Democrats.

Voters lined up from dawn to dusk all across this racially polarized city of 3.2 million. City Board of Election officials at 6 p.m. predicted an overall turnout of 88 percent.

The record turnout for a Chicago municipal election was 77 percent in the mayoral primary. In the 1944 presidential election, the turnout was 91.5 percent.

Washington is a two-term congressman and former state legislator. He was bidding to become the first black mayor in Chicago's 150-year history. Epton, 61, a millionaire lawyer and former legislator, would have been the city's first Republican mayor in 52 years.

World and national attention focused on the campaign after Washington captured the Democratic nomination by turning out a massive black vote, of which he won about 85 percent, while Byrne and Daley, both proven vote-getters, split the majority white vote.

Washington got 36.3 percent of the total vote and took a commanding 2-to-1 lead over Epton in the opinion polls. His strategists said they believed he could get about 20 percent of the white vote, enough to hold off even a serious Epton challenge and become the city's first black mayor.

But Washington's campaign stalled, buffeted by internal dissension and tough, personal attacks by Epton.

Washington snubbed former vice president Walter F. Mondale for backing Daley, and sat back waiting for reluctant Democratic Party sachems who had backed his rivals to come forward to support him as the party's nominee.

Most finally did, although some were conspicuously lukewarm. Eight white Democratic committeemen, however, defected to Epton.

Meanwhile, Epton's minuscule effort swelled with money and volunteers as many white Chicagoans sought an alternative to a black as their next mayor.

Both campaigns played on themes that helped polarize the electorate on racial lines.

Veteran political consultant John Deardourff provided Epton with the slogan: "Epton now--before it's too late!" It went down well in the ethnic wards of the southside and northwest, where integration has few sympathizers.

Washington contributed with a slogan of his own, aimed at his black supporters: "Now It's Our Turn!"

Epton also hammered at Washington's legal problems.

One was a conviction and 36-day jail term for failing to file income tax returns for four years and being delinquent $504 in back taxes. Another was a five-year suspension from practicing law for non-performance after accepting fees from clients in divorce and traffic violation cases.

Washington retaliated by accusing Epton of conflict of interest as a state legislator because of his insurance interests.