[1] Jones was signed as an undrafted free agent by the Dallas Cowboys after the 2011 NFL draft on July 28.

On November 5, he was promoted to the active roster, filling in for an injured Mat McBriar in one game against the Seattle Seahawks.

In 2012, the Cowboys decided not to re-sign McBriar and Jones entered the season as the starter at punter.

He suffered a left knee injury on September 23, against the Tampa Bay Buccaneers, when he nearly had a punt blocked.

On October 14, a practice injury to punter Brian Moorman forced him to play against the Baltimore Ravens with a partially torn ACL he was still rehabbing.

In 2015, Jones ranked third in the league with a career-best 42.5 net average, though the Cowboys required him to directional punt.

On December 7 against the Washington Redskins, he became the first punter in franchise history to recover a fumble during the return of one of his own punts.

As Roberts broke the return down the left sideline, Cowboys linebacker Kyle Wilber had the angle on him.

At the time, he had the all-time highest percentage of punts downed inside the 20-yard line (39.9%) in team history.

[9] In the fourteenth game against the Oakland Raiders, he called his own fake punt while facing 4th-and-11 on the Cowboys 10-yard line, rushing for 24 yards and a first down, that contributed to the eventual 20-17 win.

Jones had a career-best 34 punts downed inside the 20-yard line (second in team history), while registering a 41.4-yard net and a 44.1-yard gross average.

[10] On November 7, 2020, Jones was placed on injured reserve after undergoing core muscle surgery.