USC went 11-1 in singles and 5-1 in doubles in the tournament hosted by the Trojans at Marks Stadium.
Senior Angela Kulikov also reached the Round of 32 in the Singles Main Draw.
Pair made doubles consolation final, while sophomore earned singles berth in Fall Championships.
USC women's tennis will participate in the ITA All-American Championships this week as well as host the Women of Troy Invitational this weekend.
Goulak and Vagramov shined in debuts, while Johnson was unbeaten in three doubles matches.
Newcomers Goulak, Vagramov will debut at Women's Collegiate Invitational in Malibu, Calif.