LSU cornerback Morris Claiborne was considered by most to be the best defensive back available in the NFL draft.
Claiborne led the Tigers with six interceptions last season and won the Jim Thorpe Award as the nation's top defensive back. He was also LSU's top kickoff returner, averaging 25 yards per return, including a 99-yard touchdown at West Virginia.
The Cowboys were expected to focus on defense in the early rounds of the draft, with the goal of adding impact players for coordinator Rob Ryan.
Now they have used their highest draft pick since 2003, when cornerback Terence Newman was picked fifth overall, on another top cornerback.
Newman, a starter for all nine of his seasons in Dallas, was released by the Cowboys when free agency started and has since signed with Cincinnati.
Last April, during a draft complicated by the lockout, Dallas used just two of its eight picks on defenders.
The Associated Press contributed to this report.