Hopkinton High School’s field hockey and girls soccer teams hit the road Sunday and returned home victors in the Division 1 state tournament’s Round of 32.

Field hockey traveled to Brookline and came up with a 1-0 win over the 16th seed. The 17th-seeded Hillers’ reward is a Tuesday afternoon matchup at top-seeded Lincoln-Sudbury. Undefeated L-S (15-0-2) is coming off an 8-0 shellacking of Malden Catholic in its tourney opener.

Girls soccer used an offensive barrage to spark a 7-3 victory over 15th-seeded Newton South. The 18th-seeded Hillers (8-8-2) next will play the winner of Monday’s game between 31st-seeded North Andover and second-seeded Wellesley.

In other tournament action, HHS girls volleyball dropped a 3-1 decision to host Natick on Friday. The Hillers, seeded 21st, finish their season at 13-7.

Boys soccer, seeded 10th with a record of 12-4-2, opens postseason play by hosting 21st-seeded Brookline (4-6-7) on Monday at 5:30 p.m.