In 2015 as a redshirt freshman, he played in all 14 games as a backup to Austin Hooper, catching 10 passes for 121 yards and one touchdown.

[3] He helped block for running backs Christian McCaffrey and Bryce Love, while receiving honorable-mention All-Pac-12 honors.

[8] Schultz was selected by the Dallas Cowboys in the fourth round (137th overall) of the 2018 NFL Draft, to improve the depth at tight end after the surprising retirements of Jason Witten and James Hanna.

After Swaim was lost to an injury in Week 11, Schultz passed Jarwin on the depth chart as the starter and was used mostly for blocking purposes.

[13] On March 17, 2020, it was announced in the media that Witten would be leaving the Cowboys to sign with the Las Vegas Raiders, opening the door for Schultz to compete for the backup position behind Blake Jarwin.

[14] After Jarwin was lost for the year with an ACL injury suffered in the season opener against the Los Angeles Rams, Schultz took over the starting tight end position.

[15] In Week 2 against the Atlanta Falcons, Schultz caught nine passes for 88 yards and his first career touchdown reception during the 40–39 comeback victory.

[16] Schultz exceeded expectations, becoming the fourth tight end in franchise history to have at least 60 receptions in a regular season (63), while collecting 615 receiving yards and four touchdowns, even though the Cowboys lost their starting quarterback Dak Prescott in Week 5 against the New York Giants.

He opted to miss the final week of voluntary organized team activities and was a limited participant in one minicamp practice in hopes of reaching an agreement on a long-term deal, which did not happen.

The expectation was for Schultz to be close to his 2021 level of play and help reduce the blow of Amari Cooper's departure, but he was not able to achieve the same type of production.

The Cowboys also involved rookie tight ends Jake Ferguson and Peyton Hendershot in the offense, which took away some of his potential snaps and opportunities.

Schultz finished the season with 15 games appearances (8 starts), 59 catches (second in franchise history for a tight end), 635 receiving yards and five touchdowns.