It's the first defensive lineman selected since Sean Lissemore (seventh round, 2010) and the highest since they grabbed Jason Hatcher in the third round in 2006.
Crawford will add some youth and athleticism to a defensive line that currently includes Kenyon Coleman, Marcus Spears, Hatcher and Lissemore.
A JUCO transfer, Crawford became a key player for Boise State's defense last year, recording 6.5 sacks and 13.5 tackles for loss.
Crawford is the second defensive player taken this year, along with LSU cornerback Morris Claiborne, who went No. 6 overall. It marks the first time since 2005 the Cowboys took defensive players with their first two picks (DeMarcus Ware, Marcus Spears).