As a freshman, although he began the season as the third-string quarterback, Rush was named the starter by the third game, after Cody Kater was injured (collarbone fracture) and his backup Alex Niznak could not move the offense against the New Hampshire Wildcats.

The would-be final play started with a 45-yard Hail Mary pass from Rush to wide receiver Jesse Kroll.

With no space to run, Williams made a quick third lateral pass to leading receiver Titus Davis who ran the final 13 yards, scoring a touchdown that would have tied the game with a kicked extra point and sent the game into overtime, but instead Central Michigan attempted a two-point conversion for the win, which was unsuccessful.

[10] Against the Oklahoma State Cowboys, the game sparked controversy after the officials made an incorrect call that would eventually give Central Michigan the win.

However, the officials gave Central Michigan an untimed down, and Rush threw a 51-yard Hail Mary pass to Kroll, who made a lateral to fellow receiver Corey Willis at the 12-yard line, running for a touchdown with no time remaining for a 30–27 victory.

[14] Coming out of Central Michigan, Rush was projected by the majority of NFL draft experts and analysts to be a seventh round pick or a priority undrafted free agent.

[20] Head coach Jason Garrett named Rush the Cowboys' third quarterback on their depth chart, behind Dak Prescott and Moore.

Rush was promoted to second-string for the sixth game of the season, with Moore being released and signed to the Cowboys' practice squad.

[23] In 2018, Rush was the backup at quarterback from the start of organized team activities, as he never received any strong competition from rookie Mike White.

Rush only played in Week 6 against the Jacksonville Jaguars, closing out a 40–7 victory in the fourth quarter, where he only handed the ball to the running backs.

[26] On May 4, he was waived by the Cowboys after the team signed former Cincinnati Bengals quarterback Andy Dalton and drafting Ben DiNucci in the 7th round 231st overall.

[27][28] On May 5, 2020, Rush was claimed off waivers by the New York Giants, reuniting with offensive coordinator Jason Garrett, who was his head coach with the Cowboys.

[32] On October 31, 2020, Rush was signed to the Dallas Cowboys' practice squad, to provide depth after starter Dak Prescott suffered a season-ending ankle injury and backup quarterback Andy Dalton was in concussion protocol.

[33][34] Rush was elevated to the active roster on November 7 for the team's Week 9 matchup against the Pittsburgh Steelers, and reverted to the practice squad after the game.

[42] In the next game against the Washington Commanders, in his third straight start of the season, Rush completed 15-of-27 passes for 223 yards and two touchdowns with a passer rating of 107.5 during the 25–10 victory.

[50] Rush was selected as the backup quarterback behind Dak Prescott for the beginning of the 2024 season, beating out Trey Lance in preseason play.

[52] Rush earned his first win of the season in Week 12 against the Washington Commanders, completing 24-of-32 passes for 247 yards, two touchdowns, and zero turnovers as the Cowboys won 34–26.

[53] On Thanksgiving, Rush threw for 195 yards and a touchdown, extending the Cowboys' win streak against the New York Giants to eight games as Dallas won 27–20.