Kuntz is coming off an injury that prematurely ended what looked like another productive season at Old Dominion.
Washington left Penn State with the 10th most receptions in program history.
Shorter appeared in 14 games for the Nittany Lions before transferring to Florida.
Clifford becomes the first Penn State quarterback to be selected in the NFL Draft since Trace McSorley.
"This is an unreal moment, and I'm just proud."
Brown is the fourth Penn Stater to hear his name called in this year's draft.