Davenport played at UTSA from 2014 to 2017.[4][5] As a senior in 2017, he was the Conference USA Defensive Player of the Year after recording 55 tackles and 8.5 sacks.[6] During his career, he had 185 tackles and 21.5 sacks.[7]
Davenport was drafted by the New Orleans Saints in the first round (14th overall) of the 2018 NFL draft.[10] He was the second defensive end to be selected that year, behind only Bradley Chubb.[11] The pick used to select Davenport was acquired from the Green Bay Packers. On May 10, 2018, Davenport signed his rookie contract with the Saints,[12] worth $13.7 million.[13] On June 11, 2018, it was reported that Davenport injured his thumb and that it would require surgery.[14] In Week 3, against the Atlanta Falcons, Davenport recorded his first career sack in the victory.[15] In Week 8, against the Minnesota Vikings, he recorded a two-sack performance in the victory.[16] He was named to the PFWA All-Rookie Team.[17]
In a Week 2 matchup against the Los Angeles Rams in 2019, Davenport sacked Jared Goff as the Saints lost 27–9.[18]
In a Week 5 game against the Tampa Bay Buccaneers, Davenport sacked Jameis Winston twice in the 31–24 win.[19]
In week 13 against the Falcons on Thanksgiving Day, Davenport sacked Matt Ryan twice, one of which was a strip sack that was recovered by teammate Vonn Bell, in the 26–18 win.[20] On December 11, 2019, Davenport was placed on injured reserve with a foot injury.[21] He finished the season with 31 tackles, six sacks, and three forced fumbles through 13 starts.[22]
In Week 7 against the Carolina Panthers in 2020, Davenport recorded his first sack of the season on former Saints' teammate Teddy Bridgewater during the 27–24 win.[23]
The Saints exercised the fifth-year option on Davenport's contract on April 29, 2021.[24] The option guarantees a salary of $9.5 million for the 2022 season.[25] He was placed on injured reserve on September 17, 2021, with a shoulder injury.[26] He was activated on October 25.[27]
On June 15, 2022, Davenport announced he had undergone five total offseason surgeries: two on his shoulder and three on his left hand. One of the hand surgeries was to address a pinkie finger issue that had plagued him since college and involved a partial amputation of the finger.[28]
Minnesota Vikings
On March 15, 2023, Davenport signed a one-year, $13 million contract with the Minnesota Vikings.[29] The team has listed Davenport as an outside linebacker.[30] He suffered a high ankle sprain in Week 6 and was placed on injured reserve on October 16, 2023.[31]
Detroit Lions
On March 13, 2024, Davenport signed a one-year deal with the Detroit Lions. The deal has a maximum value of $10.5 million, and includes a $6.5 million base salary.[32] In a game at the Arizona Cardinals on September 22, Davenport suffered a season-ending triceps injury.[33]