Zavaleta played his freshman and senior seasons of high school soccer at Westfield High School in Westfield, Indiana. He scored 25 goals and nine assists as a freshman and 20 goals and 10 assists as a senior. He also spent his youth career with FC Pride, Real Salt Lake, and Chivas USA, and was also part of Columbus Crew's USL Super-20 championship team in 2011.
On February 7, 2011, Zavaleta signed a letter of intent to play college soccer at Indiana University. In his freshman year with the Hoosiers in 2011, Zavaleta started 22 games and led the team with 10 goals and 5 assists and was also the team leader in points with 25. He went on to be named College Soccer News All-Freshman first team, NSCAA All-Great Lakes Region first team selection, Soccer America All-Freshman first team and Chicagoland Soccer News Player of the Year.
In his sophomore year, Zavaleta started all 24 matches and again was the team leader with 40 points, with 18 goals and four assists. He led the team to their eighth national title. One of the four assists came in the 2012 College Cup final against no. 3 Georgetown, when he set up teammate Nikita Kotlov for what turned out to be the title-clinching goal. He went on to be named Big Ten All-Tournament team, NSCAA third-team All-American, College Soccer News first-team All-American and the College Cup All-Tournament team. At Indiana University he was a member of the Kappa Sigma fraternity.
On January 5, 2013, it was announced by agent Ron Waxman that Zavaleta had signed a Generation Adidas contract with Major League Soccer, making him eligible for the 2013 MLS SuperDraft. On January 17, Zavaleta was selected 10th overall by Seattle Sounders FC and immediately added to the roster. He made his professional debut on March 23, 2013, in a 1–0 loss to the San Jose Earthquakes.
On February 28, 2014, Chivas USA announced that they had added Zavaleta to their roster on loan from Seattle Sounders FC for one year. In 2014, he replaced Bobby Burling as the center back was out of play after he underwent a knee surgery.
On January 26, 2015, Toronto FC announced that they had traded their 2016 MLS SuperDraft second-round pick to Seattle for Zavaleta.
On September 5, 2015, Zavaleta scored his first goal for Toronto in a 2-1 loss against his former club, the Seattle Sounders.
Zavaleta was part of the U.S. Soccer Residency program in 2008–09 and made 23 appearances for the United States U-17 national team during that stretch, including three appearances in the 2009 FIFA U-17 World Cup. Zavaleta mostly played as a defender with the under-17s.
He is eligible to play for both the United States national team and El Salvador.
Zavaleta is the son of Carlos and Kristi Zavaleta. He has one sister, Alexa; and one brother, Casey. His father played professionally in the United States and El Salvador and was also a member of the El Salvador national team. He is also the nephew of former MLS and U.S. national team defender, and his current coach at Toronto FC, Greg Vanney.As of match played December 10, 2016
Canadian Championship: 2016, 2017
Trillium Cup: 2016, 2017
NCAA College Cup: 2012
College Soccer News All-Freshman first team: 2011
NSCAA All-Great Lakes Region first team: 2011
Soccer America All-Freshman first team: 2011
Chicagoland Soccer News Player of the Year (2): 2011, 2012
Big Ten All-Tournament team: 2012
NSCAA third-team All-American: 2012
College Soccer News first-team All-American: 2012
College Cup All-Tournament team: 2012
Soccer America MVP first team: 2012