The U.S. equestrian team vaulted from fourth to first place in the team point standings last night with a victory in the prestigious Nation's Cup Class at the Washington International Horse Show at the Capital Centre.

Before last night's event the U.S. team of riders Melanie Smith, Norman dello Joio, Peter Leone and Michael Matz had two points. The win boosted the total to 22. Switzerland, which had been leading with 13 points, is now in second place with 21.

Two rounds over 16 jumps with the best three of four riders rounds counting in the final phase determined the winning team. The United States finished with eight faults. The Canadian team (which won the class here last year) placed second with 20 faults.

Three of the four members of the U.S. squad were on the team that won the Pan American Games gold metal this summer in Puerto Rico. The fourth, Peter Leone, 19, of Franklin Lakes, N.J., made his first appearance with the team Monday night.

When asked how long he had been a member of the team he said, "Two days," then added, "I was excited before the class and I was glad we did win. Actually I was ecstatic."

Smith, 30, the only woman on the team and winner of the 1978 title of Rider of the Year, rode Calypso, a 6-year-old bay gelding. Both her rounds were faultless.

Matz rode Jet Run, the bay gelding owned by F. Eugene Dixon, of Philadelphia. He was also instrumental in the victory last night with two perfect rounds. Matz won the individual gold medal at the Pan American games.

The team from Switzerland finished in third place after gathering 24 jumping faults in the two rounds. Great Britain placed fourth with 31 1/4. In the leading international rider standings, British team member Robert Smith is in first place with eight points.