Jones attended Okeechobee High School, but because he had to work to help support his mother, he didn't play football until his junior year when he started the last 4 games of the season. He would miss all of his senior seasonfootball games, because he had to work in a drugstore during the team's summer workouts and the new head coach put in place a policy that left him out of the team. His high school athletic director sent a highlight tape of his only games as a starter to different colleges, which eventually helped him get a football scholarship from the University of Miami. He was a backup defensive end as a redshirt freshman. As a sophomore, he started the season opener at right defensive tackle. The next week he broke his hand in practice, but still managed to finish the season second on the team in quarterback pressures and posted a career-high 12 tackles against East Carolina University. As a junior, he started the final 4 games at right defensive tackle, registering 8 tackles and 2 sacks in the 23-3 win against the University of Nebraska in the 1989 Orange Bowl. As a senior, he was forced to miss spring workouts in order to earn money as a valet attendant at a restaurant, giving Cortez Kennedy the edge to start at right defensive tackle. He missed 3 games with a knee injury. He rotated with Kennedy and Russell Maryland, helping the team lead the nation in scoring defense and total defense. He finished his college career winning two national championships, while recording 105 tackles, 68 assists and 16 1/2 sacks.
Although he was a backup during his college career, Jones was selected by the Dallas Cowboys in the third round of the 1990 NFL Draft. As a rookie, he had his best year, working as the primary backup at both defensive tackle positions and starting a total of six games, with five games replacing an injured Dean Hamel. At the end of the season, he finished tied with defensive end Danny Stubbs for the team lead with 7 1/2 sacks, while adding 60 tackles, three passes defensed and 14 quarterback pressures. He also ranked sixth among all interior lineman in the NFL in sacks and was voted to the All-rookie team. Jones and DeMarcus Ware are the only rookies to ever lead or tie for the Cowboys' team lead in sacks. In 1991, he started five games at right defensive tackle. He finished the season with 33 tackles, six tackles for loss, two sacks and 10 quarterback pressures. In 1992, he started the season opener at left defensive tackle in place of an injured Tony Casillas, making five tackles, and one quarterback pressure. He also started in the third game against the Phoenix Cardinals. He finished the season with 23 tackles, four sacks, 11 quarterback pressures and one forced fumble. In Super Bowl XXVII he recovered two fumbles, including one that went for a two-yard touchdown, helping the Cowboys go ahead 14-7 in the first quarter. In 1993 he posted 5.5 sacks. He also was a part of one of the most famous Thanksgiving football plays, when he blocked a 41-yard field goal attempt from the Miami Dolphins' Pete Stoyanovich, to preserve what seemed an apparent 14-13 victory, but as the ball rolled toward the Cowboys' end zone, Leon Lett kicked the ball and the Dolphins recovered. Stoyanovich would go on to convert a second field goal with three seconds left. During his four-year Cowboys career, he helped the team win two Super Bowls against the Buffalo Bills twice, played a total of 65 games, starting 16 and recording 19 sacks. He was an effective pass rusher who got most of his playing time on passing downs, and was key backup in the best defense and best defensive line rotation in the NFL.
Los Angeles/St. Louis Rams
The Los Angeles Rams signed Jones on March 4, 1994, to a four-year contract for $7.7 million, including a $2 signing bonus. In 1994, he played in 14 games and recorded five sacks. In 1995, Jones started 16 games at left defensive tackle and did not record a sack. In 1996, he started 16 games, registering 61 tackles and 5.5 sacks. He was released by the Rams in a salary capmove on April 22, 1997.
Philadelphia Eagles
On July 23, 1997, the Philadelphia Eagles signed Jones to a one-year contract. He played only one season, posting seven tackles and 2.5 sacks in 14 games, while coming in on passing downs, a role he played while in Dallas.