ity Controller Kathy Whitmire, riding local frustration over the side effects of rapid growth, swept to an easy victory tonight to become the first woman mayor of Houston.

Whitmire, 35, defeated Harris County Sheriff Jack Heard, 63, in a runoff election after the two had defeated incumbent mayor Jim McConn in the first round of voting two weeks ago.

Whitmire, who won with about 62 percent of the vote, becomes the fourth woman mayor of a major American city, joining Jane Byrne of Chicago, Margaret Hance of Phoenix and Dianne Feinstein of San Francisco.

Her landslide victory was a signal that local politics will be increasingly dominated by newcomers who have moved from the North to make Houston the nation's fifth largest city.

Whitmire and Heard divided the city's white vote, but Whitmire scored especially well in many of the city's newest sections, a sign that her youth and businesslike approach to politics appealed to many of the city's recent immigrants.

The key to her victory margin appeared to be support in the black community. Demographic breakdowns of the returns showed that Whitmire received about 90 percent of the black vote.

Fast-growing Houston, whose population jumped 29 percent between 1970 and 1980 and whose suburbs grew at more than twice that rate, is beset with problems, including traffic jams, rising crime, inadequate mass transit and the breakdown of various city services.

The election, however, was not a referendum on growth. None of the major candidates in the original 15-person field directly challenged growth as detrimental to the city.

Whitmire crossed ideological lines in her support by combining fiscal conservatism with liberal stances on social issues.

Heard ran a single-issue campaign by promising to "stick a foot on the neck of crime," but his fuzziness on other issues cost him support among many residents.