He played college football for the San José State Spartans and was selected by the Houston Texans in the sixth round of the 2013 NFL draft.

[3] Having no scholarship offers out of high school, Quessenberry met a San Jose State assistant coach who was recruiting a teammate.

[4] Quessenberry later walked-on to the Spartans football team at San Jose State University in 2008 and redshirted that year to bulk up from his 235-pound weight.

As a freshman in 2009 under coach Dick Tomey, Quessenberry played in all 12 games mostly on special teams and was a reserve at offensive tackle and tight end.

[4] In a 1–12 season under new coach Mike MacIntyre, Quessenberry started in all 13 games at left tackle and played mostly as a punt protector and extra point lineman.

As a junior in 2011, Quessenberry again started all 12 games of the season, and San Jose State football improved to 5–7.

[1][5] On September 29, Quessenberry played in a game against Navy, a team with younger brother Paul as an offensive lineman.

[1] The Houston Texans selected Quessenberry in the sixth round with the 176th overall pick in the 2013 NFL draft.

[22] On September 15, 2019, in a 19-17 Week 2 loss to the Indianapolis Colts, Quessenberry caught his first receiving touchdown from a pass by Marcus Mariota.

[35] In June 2014, Quessenberry was diagnosed with Non-Hodgkin's lymphoma after experiencing fatigue and persistent cough.

[39] His brother Scott Quessenberry was the 155th overall pick in the fifth round of the 2018 NFL draft by the Los Angeles Chargers.