After graduating from Brazoswood High School in Clute, Texas, Tepera played college baseball at Blinn College before transferring to Sam Houston State University. In 2009, his senior season, he went 2-1 with a 7.33 ERA over 43 innings. The Blue Jays selected Tepera in the 19th round of the 2009 Major League Baseball draft. He was assigned to the Gulf Coast League Blue Jays, and made 11 appearances for the team, including 5 starts. Tepera posted a 3–1 win–loss record, 1.72 ERA, and 42 strikeouts in 36 innings. In 2010, he was promoted to the Class-A Lansing Lugnuts, and pitched 120 innings over 24 appearances. In total, Tepera earned a 9–6 record, 3.98 ERA, and 79 strikeouts. He played the 2011 season with the Advanced-A Dunedin Blue Jays, posting an 11–6 record, 4.43 ERA, and 93 strikeouts in a career-high 146 innings. Tepera started the 2012 season in Dunedin, and was later promoted to the Double-A New Hampshire Fisher Cats. He struggled during the year, and finished with an 8–6 record, 5.48 ERA, and 71 strikeouts. In the offseason, Tepera played with the Salt River Rafters of the Arizona Fall League, and made 6 starts, going 1–2 with a 6.75 ERA. Tepera played the entire 2013 season in Double-A New Hampshire, bouncing back with a 10–8 record, 4.50 ERA, and 105 strikeouts in 116 innings. 2014 saw Tepera make his first trip to the Triple-ABuffalo Bisons, where he pitched exclusively as a reliever. In 51 games, he posted a 7–3 record, 3.66 ERA, and 67 strikeouts in 64 innings pitched. The Blue Jays added Tepera to their 40-man roster on November 20, 2014 to protect him from the Rule 5 draft. He began the 2015 season with the Buffalo Bisons, and was promoted to the major leagues by the Blue Jays on May 8.
Tepera made his debut on May 10, 2015, against the Boston Red Sox. He pitched 2 innings in relief of R.A. Dickey, and did not allow a baserunner, while striking out 1. Tepera was optioned back to Buffalo on August 1, and recalled on September 1. He earned his first save on September 12, closing out a 9–5 win over the New York Yankees. Tepera was initially left off of the postseason roster, however he was added on October 10 after Brett Cecil suffered a season-ending calf injury the day prior. After participating in 2016 Major League spring training, Tepera was announced on March 30 as one of the Blue Jays bullpen pitchers for Opening Day. However, shortly afterward the Blue Jays signed Franklin Morales and optioned Tepera to Triple-A Buffalo. On April 27, Tepera was recalled from Buffalo. After taking the loss against the San Francisco Giants on May 11, Tepera was optioned back to Triple-A Buffalo. He was recalled on May 30, and optioned again on June 5. On July 24, Tepera was recalled after Drew Storen was designated for assignment. Tepera was returned to Buffalo on July 26. He was recalled on August 10, and optioned back to Buffalo on August 23. After the Major League roster expansion on September 1, Tepera was called up by Toronto. After spring training, Tepera made the 2017 Opening Day roster. On April 21, he earned his first career win after pitching three shutout innings against the Los Angeles Angels of Anaheim. Tepera finished the 2017 season with a 3.59 ERA and 81 strikeouts over 77 innings. He began the 2018 season as the setup man to closer Roberto Osuna. He was placed on the disabled list on June 30 with elbow inflammation. Tepera finished the season with a 5–5 record in 68 games, striking out 68 in innings.
Chicago Cubs
Tepera was designated for assignment on November 4, 2019. He elected free agency four days later. On December 20, he signed a one-year deal with the Chicago Cubs.
