Enunwa attended Rancho Verde High School in Moreno Valley, California. He was selected All-Inland Valley League first-team in high school. He played football and ran track. As a senior, he caught 40 passes for more than 600 yards and 15 touchdowns. He was selected and played in the Inland Empire All-Star Game while in high school. In addition to football, he competed as a jumper on the school's track & field team. He finished sixth in the triple jump at the 2009 CIF-Southern Meet, setting a personal-best leap of 13.79 meters. He won the high jump at the 2010 Rancho Verde Relays of Champions, with a career-best jump of 2.06 meters.
College career
Enunwa was named to the Nebraska Scholar-Athlete Honor Roll in his junior season. He was selected as the 2014 TaxSlayer.com Gator Bowl MVP and was also the Nebraska Offensive MVP in his senior season. In the 2013 season, Enunwa broke Heisman Trophy winner Johnny Rodgers's school record for most touchdown receptions in a season, catching 12 touchdowns in his senior year. At the 2014 TaxSlayer.com Gator Bowl, Enunwa broke the Nebraska school record for longest reception, by scoring a touchdown on a 99-yard reception from quarterback Tommy Armstrong Jr. in the third quarter.
Professional career
The New York Jets selected Enunwa in the sixth round of the 2014 NFL Draft on May 10, 2014.
2014
On May 15, 2014, the New York Jets signed Enunwa to a four-year, $2.29 million contract that includes a signing bonus of $78,680. He was released by the team on September 1, 2014 and signed to the team's practice squad a day later. Enunwa was promoted to the active roster on December 27, 2014. During his rookie year in 2014, Enunwa played in only one game, which was in Week 17 against the Miami Dolphins, and did not record any statistics. On October 19, 2015, Enunwa was suspended for four games of the 2015 season without pay due to violating the NFL Personal Conduct Policy.
2015
On November 21, Enunwa was re-activated from his suspension. During the 2015 season, he played in 12 games and recorded 315 receiving yards.
2016
With the Jets being short-handed on tight ends in 2016, the team announced that Enunwa would be the slot receiver and an end-around sweep specialist. In 2016, Enunwa has had a breakout year filling in for the injured wide receiver Eric Decker, coming second in receptions, yards, and touchdown receptions on the team. Enunwa posted a quality performance on Thursday Night Football in Week 2 against the Buffalo Bills on September 15, 2016 when he had six receptions for 92 yards in the 37–31 victory. Enunwa had a great third season, having totals of 58 catches, 857 yards, and four touchdowns.
2017
On August 7, 2017, Enunwa was placed on injured reserve with a neck injury. It was eventually revealed that Enunwa was diagnosed with bulging discs in his neck, and that aftermath of surgery could require from six to nine months to recover.
2018
Enunwa returned healthy in 2018, recording 38 receptions for 449 yards and one touchdown. He was placed on injured reserve on December 29, 2018. On December 28, 2018, Enunwa signed a four-year, $36 million contract extension with the Jets through the 2022 season.
2019
On September 11, 2019, it was announced that Enunwa would miss the remainder of the season after suffering a neck injury in the first quarter of the Jets' season-opening loss to the Buffalo Bills.
2020
On May 5, 2020, the Jets announced that Enunwa would miss the entire 2020 season and was placed on the reserve/physically unable to perform list.