Eluding a core of anti-apartheid protesters who had vowed to stop them, the South African national rugby team, the Springboks, played their first match on American soil today, easily defeating a team of Midwestern All-Stars, 46 to 12.

Playing before an early-morning, beer-drinking crowd of about 500, the Springboks outran, outkicked and outtackled their American opponents on a field here at the shore of Lake Michigan in a game that is likely to have major implications for the international sports community.

The game was interrupted once by protests, but only briefly. Midway through the second half, about a half-dozen protesters walked onto the field, but match organizers quickly hustled them off. As play resumed, one of the protesters was punched, kicked and knocked to the ground, then dragged off to a nearby policeman who arrested the protester for disorderly conduct.

Minutes later another protester, Marv Heppel, a member of the Racine school board, reappeared on the field but was promptly dragged off and arrested without causing any halt in play. Heppel called the match a political event and said he was protesting the use of the field, a city park, for it.

The time and place of the match, organized by the Midwest Rugby Football Union, had been kept secret in an effort to thwart a coalition of Chicago-based civil rights and religious organizations which hoped to keep the match from being played. The coalition is protesting South Africa's racial policy of apartheid.

Just after dawn today, members of the Springbok team left their quarters at the Chicago Athletic Association in downtown Chicago, boarded three vans and sped off. They were followed to Racine, about 65 miles north of Chicago, by a crew of reporters and observers for the protesters, who have kept the Springboks under surveillance since their arrival in this country Monday.

Meanwhile, in Chicago, an organization called Stop the Apartheid Rugby Tour (SART) dispatched busloads of protesters to the game site, but the first bus did not arrive until just after the game ended. Nevertheless, said a SART spokesman, "We consider it a victory. We forced them to run and hide."

But members of the rugby union also claimed victory because the game was completed.

"This is wonderful. It was a wonderful game," said Edmund Lee, a coordinator of the tour. Lee said the Springboks will play two games in New York before returning to South Africa, but he would not comment further on their itinerary.

A hearing is scheduled Monday in U.S. District Court in Albany on a request by the Eastern Rugby Union for an injunction against the cancellation by New York Gov. Hugh Carey of a Springbok match scheduled Tuesday in a city-owned stadium in Albany.

Today's match with the Springboks had been actively opposed by the U.S. Olympic Committee, which fears repercussions for the 1984 Olympics scheduled for Los Angeles.