[9] On November 1, against South Carolina, Barnett had a season-high three sacks to go along with five total tackles in the overtime win at Williams-Brice Stadium.

[13][14][15][16] Both Barnett and Myles Garrett, of Texas A&M broke Jadeveon Clowney's SEC freshman sack record, which had previously been 8.0.

[21] Against Alabama in their annual rivalry game, Barnett recorded a sack against the eventual National Champions at Bryant–Denny Stadium in a narrow 19–14 loss.

[24] In 2016 Outback Bowl against Northwestern, Barnett had eight total tackles and a sack in the 45–6 victory at Raymond James Stadium in Tampa, Florida.

[27] In the annual rivalry game against SEC East rival Florida at Neyland Stadium, Barnett had five total tackles and two sacks in the Volunteers's first victory over the Gators since 2004.

[28] Against Georgia at Sanford Stadium, Barnett had five total tackles and two sacks for the second straight game, and in addition, recorded a crucial forced fumble, off of quarterback Jacob Eason, that was recovered by teammate Corey Vereen for a defensive touchdown.

[30] Against Alabama the following week, Barnett had three total tackles, a sack, and an interception off of quarterback Jalen Hurts in the Volunteers' 49–10 home loss.

He received an invitation to the NFL Combine, but opted to skip the bench press, short shuttle, and three-cone drill due to a stomach bug.

[38][39][40][41] The Philadelphia Eagles selected Barnett in the first round (14th overall) of the 2017 NFL draft, using the pick acquired by trading Sam Bradford to the Minnesota Vikings.

[47] He competed with Brandon Graham, Chris Long, Vinny Curry, and Steven Means throughout training camp for a job as a starting defensive end.

Head coach Doug Pederson named him the backup right defensive end behind veteran Vinny Curry to start the regular season.

[48] He made his professional regular season debut during the Eagles' season-opener again the Washington Redskins and recorded two solo tackles in a 30–17 victory.

[49] In Week 6, Barnett collected two solo tackles and was credited with half a sack on Carolina Panthers quarterback Cam Newton during a 28–23 victory.

[55] The Philadelphia Eagles finished atop the NFC East with a 13–3 record, clinching home field advantage and a first round bye.

On January 13, 2018, Barnett appeared in his first career playoff game and helped the Eagles defeat the Atlanta Falcons 15–10 in the NFC Divisional Round.

[56] The following week, Barnett had two solo tackles and had a strip sack on quarterback Case Keenum during a 38–7 victory against the Minnesota Vikings.

[61] In the 2019 season, Barnett appeared in 14 games and recorded 6.5 sacks, 30 total tackles, 10 tackles-for-loss, 22 quarterback hits, and two forced fumbles.