Chivas scored the game's first goal in the 34th minute when David Izazola slipped Rivera behind the backline, and Rivera finished into the far upper corner.
Rivera doubled the lead just three minutes later when his free kick from 25 yards out dipped over the wall and landed inside the near post.
Sounders FC pulled one back in the 44th minute on a goal from Zavaleta. David Estrada beat his defender down the right flank and sent a low cross into the box that Zavaleta tapped into an open net.
Seattle equalized in the 63rd minute on a penalty kick from Servando Carrasco. Chivas' Emilio Orozco was whistled for a handball in the box after he deflected Andy Rose's header, and Carrasco converted the penalty kick to level the score at 2-2.
Sounders FC netted the game-winner in the 81st minute on Zavaleta's second goal of the game. Dylan Remick took a quick throw-in on the left side and found Zavaleta behind the Chivas backline. Zavaleta flicked the ball over the onrushing keeper to put Seattle ahead, 3-2.
Zavaleta had a handful of other scoring opportunities, including a pair of shots in the final minutes of the first half that forced Patrick McLain into diving saves.
Chivas' Julio Morales had a breakaway shot saved in the 24th minute by Doug Herrick, and three minutes later Morales' shot from inside the box was blocked by his defender.
Seattle's next reserve league match is on August 11 against Orlando City SC at the Citrus Bowl while Chivas USA hosts the Colorado Rapids on August 12.
CHV - Jose Manuel Rivera (David Izazola) 34'
CHV - Jose Manuel Rivera 37'
SEA - Eriq Zavaleta (David Estrada, Servando Carrasco) 44'
SEA - Servando Carrasco (penalty) 63'
SEA - Eriq Zavaleta (David Estrada) 81'
Seattle Sounders FC - Doug Herrick, Cody Crook, Ashani Fairclough, Zach Scott (Jhon Kennedy Hurtado 45), Dylan Remick, Will Bates (Henry Wingo 73) , Servando Carrasco, Blair Gavin (Andy Rose 45), Youseff Adnane (Jordan Morris 45), David Estrada, Eriq Zavaleta.
Substitutes Not Used: Bryan Meredith, Duncan McCormick.
TOTAL SHOTS: 19; SHOTS ON GOAL: 10; FOULS: 10; OFFSIDE: 2; CORNER KICKS: 5; SAVES: 4.
Chivas USA - Patrick McLain, Josue Soto, Jaime Frias, Steven Purdy, Emilio Orozco, Julio Morales (Bryan de la Fuente 59), Jose Rivera, Aaron Ponce, Marvin Iraheta, Eric Avila (James Alecoine 86), David Izazola.
Substitutes Not Used: Michael Abalos.
TOTAL SHOTS: 14; SHOTS ON GOAL: 6; FOULS: 12; OFFSIDE: 2; CORNER KICKS: 7; SAVES: 7.
CHV - Jaime Frias (caution) 48'
CHV - Marvin Iraheta (caution) 70'
CHV - Aaron Ponce (caution) 84'
SEA - Jordan Morris (caution) 90+
Referee: Chipalo Street
Referee's Assistants: Jeremy Hanson; Ian Johnson
4th Official: Levi Rippy