Dobbs entered the 2016 season as Tennessee's starting quarterback in his final season of collegiate eligibility. He started and appeared in all 12 regular season games and the bowl game. Dobbs started the season with a solid performance in a home game against Appalachian State. In the 20–13 overtime win, Dobbs had 192 yards passing but fumbled on the goal line; the ball was recovered by teammate and running back Jalen Hurd to give Tennessee the go-ahead score. In the 2016 Pilot Flying J Battle at Bristol, Dobbs three passing touchdowns to go along with two rushing touchdowns. In a 38–28 comeback victory over the #19 Florida Gators, Dobbs had 319 yards passing, four passing touchdowns, 80 rushing yards, and a rushing touchdown to lead the Volunteers to their first win over the Gators since 2004. Against #25 Georgia, Dobbs had 230 yards passing, three passing touchdowns, and a rushing touchdown to win 34–31. Dobbs's last touchdown was a Hail Mary throw to wide receiver Jauan Jennings as time expired. The winning play is referenced by many as the "Dobbs-Nail Boot". With the victory, Tennessee was 5–0 with Dobbs as quarterback and ranked as high as top 10 in some polls. In a 2OT 45–38 loss to the #8 Texas A&M Aggies at Kyle Field, Dobbs had a season-high 398 passing yards and one passing touchdown. In addition, he caught a receiving touchdown from Jauan Jennings, his second career receiving touchdown. Dobbs continued solid performances over the rest of the season: he had five touchdowns, 223 passing yards and 190 rushing yards in a 63–37 win over Missouri and 340 passing yards in a 45–34 loss against Vanderbilt at Vanderbilt Stadium. Despite his play, Tennessee faded from their 5–0 start to finish 8–4.
In the final game of his Tennessee career, Dobbs led the Volunteers past the #24 Nebraska Cornhuskers by a score of 38–28 in the 2016 Music City Bowl at Nissan Stadium in Nashville. He had 291 passing yards, one passing touchdown, 11 rushes for 118 yards, and three rushing touchdowns. Dobbs was named the MVP of the game.