Henry Cisneros, a 33-year-old urban planner, swept to victory here tonight to become the first Mexican-American mayor of a major American city.

Cisneros, a champion of economic development, turned aside a well-financed campaign by John Steen, a 59-year-old businessman and civic leader, to win the race without a runoff.

With all but one of the 217 precincts reporting, Cisneros had 62 percent of the vote to Steen's 36 percent. Six other candidates accounted for the remainder of the vote.

Cisneros was aided by a strong turnout among Mexican Americans, who make up 54 percent of the population here, but assured his easy victory by attracting more than 40 percent of the votes in the three main Anglo districts.

"This is a victory for all the people of San Antonio," a beaming Cisneros told hundreds of supporters at his campaign headquarters. "It's a victory to move the city forward."

The contest had been billed as old versus new: old money against new money and, more significantly, Old Santonio against New San Antonio. The nigth largest city in the United States, San Antonio represents the growing power of Mexican Americans in the politics of the Southwest.

Cisneros worked diligently to get the heavy turnout among Mexican Americans, and improved his chances with an appeal to Anglo voters to join him in leading the city forwardd through continued growth.

He also does not fit the mold of many Mexican-American politicians and is generally viewed as more moderate and less ethnically oriented than other Hispanic officeholders.

Both Cisneros and Steen are members of the City Council in a town with a weak-mayor form of government. But Cisneros campaigned as an activist who would attempt to make the mayor the dominant force in city government, while Steen advocated a more traditional approach to running the city.

Cisneros, a councilman since 1975, was heavily favored to win the mayor's race a few months ago. A White House fellow during the Nixon administration, assistant city manager in two cities and urban planner by academic training, he had long been pointing toward the race.

Early in the campaign he lined up the support of key developers in town, who provided him with financial assistance and a bridge to the business community. At that point, with his position among minorities and labor well grounded, the race looked like a walkaway.

But then Steen hired the Washington political consulting firm of Bailey & Deardourff and a phone bank expert from Minnesota, and quickly turned what had been expected to be a coronation into a lively -- and occasionally bitter -- race.

Media adviser John Deardourff put together an advertising campaign designed first to build up Steen in the eyes of voters and then attack Cisneros. The negative ads quickly became the most controversial aspect of the election. As political ads go, they were not especially negative, but they hurt Cisneros enough to put Steen back into the fight.

One ad accused Cisneros of selling out to the developers. Another charged that Cisneros was unreliable, inconsistent and made conflicting promises to different audiences.

Cisneros's campaign staff cried foul and said Steen was trying to exploit the racial issue in one of the ads, and Cisneros called a news conference to issue a bitter, rambling attack against Steen and Deardourff, decrying the use of outside consultants.

But the ads also tarnished Steen's image as a decent community leader and may have cost him some support.