Danny Goldie and Jenny Goodling captured the singles titles at the National Amateur Indoor Tennis Championships at the Crystal City Racquet and Health Club yesterday.

The 14th-seeded Goldie, formerly of Bullis Prep, stopped the tournament's unseeded sensation, 17-year-old John Zahurak of Calvert Hall in Baltimore, 6-4, 6-2. Goldie said, "I relied on my usual game plan of a strong return of serve and good passing shots."

Zahurak led 4-3 in the first set and 2-1 in the second after service breaks, but each time Goldie broke back quickly and then served for the leads, which he maintained. The victory was Goldie's first in a major amateur tournament after an excellent 1982 junior season in which he was ranked third nationally in the 18-and-under category.

Goldie, who will play No. 2 for powerful Stanford as a freshman this spring, has never lost to Zahurak and his booming returns to Zahurak's forehand gave him the victory yesterday. "I was returning well today and I kept him away from the net," said Goldie.

Third-seeded Goodling, Rollins College's top player, used an excellent forehand and well-placed volleys to overpower defending champion Kathleen Cumings of Richmond, 6-4, 6-0. The turning point came with Goodling serving at 5-4, love-30, in the first set. Cummings, an all-America at Colorado before transferring to Texas, blew an easy winner to allow Goodling back into the game she eventually won for the set.

"I played two sorry points to love-30," Goodling said. "If I had lost that game, I might have lost the set and maybe even the match." Goodling lost only one set in the tournament.

Norm Schellenger and Stevenson Clarke of Washington rallied from a disastrous first set to win the men's doubles title, 2-6, 7-6, 7-6, over Tennessee's Paul Annacone and Earl Grainger.

Princeton's pair of Joy Cummings and Jan Shelburne, formerly of Whitman High School, won the women's doubles final, 7-5, 7-5, over Caryn Schindler of Kennedy High School in Silver Spring and Annandale's Carol Daniels.