The D.C. City Council turned back a last-minute surge of lobbying by some black business owners and gave final approval yesterday to a bill that would include Asian Americans, Pacific Islanders and Hispanics of European descent in the city's $140 million-a-year minority contracting program.

The measure was approved after some council members, accompanied by unruly outbursts from the audience that filled the council chambers, exchanged sharp comments on racial discrimination.

"I'm not about to turn my back on the black community," said council member H. R. Crawford (D-Ward 7), a long-time supporter of the bill who said he decided to oppose it after being deluged with telephone calls, telegrams and personal visits to his office.

"Some of you have forgotten that our families were flogged and beaten," Crawford, who is black, told the council at one point.

John Ray (D-At Large), who supported the bill, shot back, "I knew I was black when I voted the first time." Ray told Crawford that he did not have "to duck and dive in response to political pressure, as obviously you are."

The council approved the bill on an 8-to-3 vote after rejecting one amendment by Wilhelmina J. Rolark (D-Ward 8) to table the issue until December and another by Crawford to restrict access to the program to those who could prove they had suffered discrimination here.

Voting against the measure were Crawford, Rolark and Nadine P. Winter (D-Ward 6). William R. Spaulding (D-Ward 5) voted present and Jerry A. Moore Jr. (R-At Large) left before the vote to take part in a dedication ceremony at the University of the District of Columbia.

The measure was initially approved in 1976 in response to complaints that although the city's population was 70 percent black, minority firms were receiving few of the millions of dollars spent by the city government each year.

Supporters of the measure approved yesterday contended that extension of the program to others would only be in keeping with the spirit of the original law.

"If our basic goal is to discriminate against those who are not black, then that's racism of the worst kind," said John A. Wilson (D-Ward 2), a sponsor of the expansion bill who said some of the remarks made about Asians and Hispanics "are absolutely insulting. If they were said about us, we would not take it very kindly." Wilson is black.

Council Chairman Arrington Dixon several times had to caution the audience against outbursts that included handclapping and derisive comments against Wilson and others who supported the bill.

The council's action yesterday reverses a 1980 vote that deleted Asians from the program and restricted Hispanic involvement to those persons from Central and South America, the Caribbean and Mexico.

Hispanics of European descent, many of whom were considered too wealthy or not subject to historic discrimination suffered by other minorities, were eliminated from the program.

The bill now defines minority as "Black Americans, Native Americans, Asian Americans, Pacific Islanders and Hispanic Americans who by nature of being members of the foregoing groups, are economically and socially disadvantaged because of historical discrimination practiced against these groups by institutions within the United States of America."

The minority contracting program currently sets aside up to 25 percent of the money that the city spends on goods and services and construction for certified minority-owned firms.

The measure approved yesterday expanding participation in the program also expands from 25 percent to 35 percent the portion of annual expenditures that should be reserved for minority groups covered by the law.

Carroll B. Harvey, who resigned as head of the District's Department of General Services last year and now heads an asphalt manufacturing firm here, said yesterday he was among several black businessmen who organized the protest to the bill.

Harvey said black business owners failed to actively oppose the bill before the council gave the measure preliminary approval two weeks ago and that the change would hurt black businesses in the District.