Eberle posted three goals and three assists, and Eldredge scored three times and registered two assists to lead the Broncos to a 13-8 road win against the Seawolves (0-4) who were held to only one goal for a 13-minute stretch of the second half.
Annika Erickson had four goals and JoJo Williams chipped in three to lead the Sonoma State offense, which was efficient (eight goals on 17 shots) but didn't generate attempts.
The Broncos (3-6) were able to create 38 attempts on goalkeeper Brooke Sullivan who posted 13 saves in the loss.
A goal by Williams with 48 seconds left in the second quarter closed the Sonoma State deficit to 4-3, but Eberle set up a Kelly Frumkin score just before halftime to start an 8-1 run for the Broncos.
Eberle scored twice and Eldredge once in 1:08 span of the fourth quarter to increase the Santa Clara lead to 11-4 and the Seawolves were never closer than the final margin.
Santa Clara lost its final three games at last weekend's Triton Invitational after leading in the final period.
"The best part of the game was our fourth quarter, and that is where we needed to improve from last weekend," Santa Clara head coach Keith Wilbur said. "I really liked our composure when the game was tight."
Eldredge (six) and Eberle (four) combined for 10 of the team's 19 steals. Lydia Dadd, who made seven saves and surrendered four goals to pick up the win, also had five steals.
Lauren Paxton had one goal and two assists for the Broncos who were 6-for-12 with the man advantage.
• Hannah Buck, Emma Allegrucci, Annie Eldredge, Lauren Paxton, Maggie Oys, Hailey Eberle and Lydia Dadd comprised the starting lineup. Buck, Allegrucci, Eldredge, Paxton and Eberle have started all nine games.
• Eldredge's six steals and five for Dadd were career-highs. Eberle's four steals matched a career-best.
The Broncos will make their first home appearance on Saturday by serving as the hosts of the Santa Clara Invitational. The Broncos will face Cal State Monterey Bay at 9 a.m. and UC Davis at 3 p.m. in Sullivan Aquatic Center. Those two teams will face off at noon.