THERE WAS SOMETHING altogether fitting - and instructive, as well - about the presence of Secretary of State Cyrus Vance yesterday at the inauguration of Antonio Guzman as the new president of the Dominican Republic. It was fitting in the sense that, off and on, Mr. Vance has been working personally on the Guzman case for 13 years. And it was instructive for what it says about the American involvement in the fortunes of the Dominican Republic - its extraordinary depth, its chaning nature and even its future prospects.

The Vance-Guzman connection began in the terrible turmoil of the Dominican civil war in 1965, when there was no authority and American troops had been landed to restore order in the name of anticommunism. Mr. Vance, as deputy secretary of defense, was a member of high-level team of American mediators dispatched by President Johnson to Santo Domingo to assemble a compromise, caretaker government, with Mr. Guzman as the provisional president. That frenzied, around-the-cock effort eventually collapsed. But it paved the way for a more measured American diplomatic intervention, the eventual result of which was the election to the presidency of Joaquin Balaguer (also hand-picked in Washington).

With lavish and unwavering support from the United States, Mr. Balaguer managed, by means of more or less benevolent repression, to get reelected twice without real opposition or any serious challenge to his methods until last spring's presidential election. Then Mr. Guzman won a comfortable majority of the vote, and very nearly had the election stolen found him by elements in the Dominican armed forces loyal to Mr. Balaguer.

At which point, reenter Mr. Vance, as secretary of state for Jimmy Carter; while too much can be made of the importance of the Carter administration's intervention - for there was a powerful outcry from within the Dominican Republic - it is certain that pressure from Washington had much to do with keeping the vote-counting honest. The result, celebrated yesterday in Santo Domingo, was the first peaceful, constitutional transfer of power from one elected government to another in the Dominican Republic's history.

That is no small accomplishment for a country that emerged in 1961 from 30 years of tyranny under Trujillo to elect Juan Bosch as president, only to see him thrown out in a military coup aftter seven months in office, and his unelected successor similarly unseated in the bloody upheaval of 1965. Indeed, there are many who saw in the events last spring compelling evidence of fundamental change - of strong and widespread support for a fair election and a democratic form of government, from business elements and opinion-makers and the public. Perhaps. It will depend, we suspect, in large part on the Dominican military. In part, it will also depend on the skill and forcefulness of President Guzman, a man of the left, whose connections with military are not quite as dependable as those of Mr. Balaguer, a man of the Trujillo regime. But it will almost certainly continue to depend, in considerable part, on the role played by the the U.S. government. Years of deep involvement have created a special American obligation to uphold democratic values in the Dominican Republic - an obligation appropiately acknowledged by the highlevel American representation at yesterday's inaugural ceremonies.