It's the second time in four drafts that Dallas has taken a cornerback in the first round. The Cowboys traded up to get Morris Claiborne at No. 6 in 2012, but he has underperformed in three seasons and isn't expected to be ready for training camp because of a knee injury.
Dallas signed Brandon Carr to a $50 million contract in free agency the same year that Claiborne was drafted, and he had a subpar 2014 season.
Jones played the first seven games of last season before a lingering shoulder injury sidelined him for the rest of the year. He had eight career interceptions at UConn.
The Cowboys lost NFL rushing champion DeMarco Murray to NFC East rival Philadelphia in free agency, but Georgia's Todd Gurley and Wisconsin's Melvin Gordon were gone by the time Dallas picked.
While they improved dramatically on defense in 2014, the Cowboys still had a mediocre pass rush and signed free agent defensive end Greg Hardy from Carolina even though he faced a season-opening suspension that ended up being 10 games.
Executive vice president Stephen Jones said Dallas wasn't surprised by the length of ban for Hardy, who was penalized for his role in a domestic violence case. The Cowboys also are just a year removed from trading up to early in the second round for DeMarcus Lawrence, who broke a foot in training camp and missed half of his rookie season.
The Cowboys lost linebackers Bruce Carter and Justin Durant in free agency, but re-signed former top 10 pick Rolando McClain after he revived his career with a solid season despite some issues with injuries. Sean Lee also is expected back after missing 2014 with a torn knee ligament.
The Cowboys went in with the same draft position they had as defending NFC East champs in 2010, when they moved up three spots to get Dez Bryant.
Dallas drafted offensive linemen first in three of the past four drafts, and last year guard Zack Martin became the team's first rookie All-Pro since Calvin Hill in 1969.