Kiper and Todd McShay faced off in a mock draft televised on ESPN2 with Kiper making selections for the team with the even-numbered picks and McShay handling the odd-numbered picks.
Six wide receivers were taken in the first 18 picks and just two cornerbacks were off the board when Kiper made the Steelers' pick.
McShay took Michigan State cornerback Trae Waynes for the Minnesota Vikings at No. 11. Kiper surprised Bill Polian and Louis Riddick, who analyzed the picks, by selecting Washington cornerback Marcus Peters at No. 20 for the Philadelphia Eagles.
Johnson was the next cornerback drafted with Kiper taking him at No. 26 for the Baltimore Ravens.
Jones is off the charts in measurables and character and the 6-1, 199-pounder played safety at UConn before moving to cornerback his final two seasons. Jones missed the final five games last season after undergoing shoulder surgery so he would have to check out medically for the Steelers to take him at No. 22.
"I love versatility, I love a guy who makes plays throughout his career," Kiper said of Jones. "He has a ton of experience and the Steelers need help desperately in the secondary."
Among the players Kiper passed on for the Steelers were Johnson, Missouri outside linebacker Shane Ray, Clemson outside linebacker Vic Beasley, Alabama safety Landon Collins and LSU cornerback Jalen Collins.
Neither Beasley nor Landon Collins, who visited the Steelers on Wednesday, were taken in the first round