MONTPELIER, VT., MARCH 1 -- Massachusetts Gov. Michael S. Dukakis won his third New England presidential nominating contest in the Vermont primary tonight, and Jesse L. Jackson picked up his second second-place finish in a state with a minuscule black population.

On the Republican side in this "beauty contest" primary, where no national convention delegates are at stake, Vice President Bush scored a victory over Senate Minority Leader Robert J. Dole (Kan.), despite Dole's endorsements from three key party leaders.

With 98 percent of the precincts reported, Dukakis had 56 percent of the vote and Jackson had 26 percent. The other candidates were far behind in single digits. Among Republicans, Bush was leading Dole 49 to 39 percent, and Dole's supporters had conceded the race. The other Republicans were in single digits.

"I think the size of the Dukakis victory far exceeds our expectations," said Gov. Madeleine M. Kunin, Dukakis' chief backer here. "I think it gives him a real boost going into the South."

Jackson supporters said the results are important because they show he can win white votes. "This is the whitest state in the country," said Jackson state campaign coordinator Liz Blum. "No one expected us to do anything in Vermont."

On the Republican side, Dole ran with endorsements from three of the most visible Republicans in the state: Sen. Robert T. Stafford, Rep. James M. Jeffords, and former governor Richard Snelling.

Because there is no party registration in Vermont, and because voters may cast ballots in either the Democratic or Republican contests, the race here was seen by some as a test of Dole's claim that he among the Republican candidates is best able to draw support from independents and Democrats.

"This is a place Dole had to win to prove his point," said Ron Kaufman, Bush's Northeast campaign director. "If he can't beat us here, he can't beat us anywhere."

Mary Ellen Grupp, vice chair of Dole's state campaign, said, "I think we finished a strong second. We showed that Dole is a candidate with more than regional appeal."

Vermont will choose 17 Republican convention delegates and 14 Democratic convention delegates at caucuses in April.

"We continue to grow; our message continues to win. We have found a common chord that links the American people," Jackson said from his mother's house in Greenville, S.C.

Jackson's national campaign office had bought television advertising here and his local volunteer organization had purchased radio and newspaper ads.

Dukakis, who also advertised on television, said of his victories, "Sunday in Maine and today in Vermont, our message prevailed."

While Dukakis employs a paid staff of 15 that has been working out of a Burlington office since January, Jackson volunteers who remained active since the 1984 primaries have been working with farmers in the troubled dairy industry and supporting candidates for local and state legislative offices over the last four years.

The campaigns of Democrats Sen. Paul Simon (Ill.), Rep. Richard A. Gephardt (Mo.) and former senator Gary Hart (Colo.), who won here four years ago, and Republicans Rep. Jack Kemp and former television evangelist Pat Robertson made little effort here.