Alexander Kuzmin, a 27-year-old e'migre' from the Soviet Union, won the $10,000 first prize in the University of Maryland International Piano Competition Saturday night with a strikingly assured performance of that classic of contest vehicles, Tchaikovsky's First Concerto.

The judges rendered a quick verdict after Kuzmin and the other two finalists performed concertos at the Tawes Theatre with the Festival Orchestra, a free-lance group, under the direction of Eve Queler, the conductor of the Opera Orchestra of New York.

Second prize of $5,000 went to 29-year-old Israeli pianist Liora Ziv-Li, who played an intense and beautifully molded interpretation of the Beethoven Third Concerto. Third prize, which carried $2,500, was won by 28-year-old French pianist Remy Loumbrozo, who played a lyrical version of the huge Brahms First Concerto.

The concert capped the eight-day competition in which a field of 40 entrants was reduced to 15 semifinalists on Monday, and to the three finalists on Friday.

The speed of the decision seems to suggest that there was little, if any, doubt among the judges about the choice of the first-prize winner. But the audience reaction suggested that many felt otherwise. Though Kuzmin drew spirited applause, Ziv-Li's playing, which came last, drew a considerable ovation. A large part of the audience was standing and cheering as she returned repeatedly for bows after the Beethoven.

On the whole, Kuzmin's performance was cooler than Ziv-Li's. But that is not to say that it was at all bloodless or lacking character. Kuzmin listed Gary Graffman as one of his teachers, and the interpretation's classic reserve resembled Graffman's own recording of the concerto. Technically, the performance was most impressive. Extraordinarily difficult passages like the vollies of double octaves in the first and last movements were perfectly clean. Kuzmin, who is a product of the Tchaikovsky Conservatory in Moscow and the Manhattan School of Music, has tremendous power, as in the last-movement cadenza, but he does not overuse it.

It was not hard to see why the audience was so taken by Ziv-Li's playing. She has a superb tonal command, and she phrased with utter authority, conveying a compelling sense of mood at all times, especially in the rapt slow movement. In most senses, this was top-notch Beethoven, and the orchestra played better here than otherwise. So why did she not win?

One reason, perhaps, was that she had a few too many conspicuous wrong notes, several of them right on the main melodic line. No doubt they came from nervousness, which contrasted with Kuzmin's apparent nerves of steel. Also, there were accents, especially at the tops of some first-movement scale passages, that seemed mannered. The accents broke the line of the music, a curious thing to do given the evenness of Ziv-Li's runs.

Loumbrozo's Brahms lacked the bravura that some pianists bring to this score. And he was technically a little shaky in the first few minutes. But once he caught his stride, the interpretation was sensitive and sophisticated. The slow movement, in particular, was wonderfully poetic. The sound that he produced was unfailingly lovely, and the agility in the knuckle-bending finale was impressive.

First prize includes some opportunities for concerts and recordings.