Having started on a positive note, racing to 41 for no loss in five overs, Tuskers suddenly plummeted to 73 for four in 10.1 overs to hand the advantage to the Royal Challengers.
McCullum, who threatened to cut lose, was the first to depart, chipping Daniel Vettori to substitute Arun Karthik, fielding in place of the injured Cheteswar Pujara.
Klinger joined McCullum back in the hut, playing all over a Chris Gayle delivery to have his stumps rattled.
Much was expected of Jayawardene, but the captain was snaffled behind the wicket by AB de Villiers off the canny Vettori. Parthiv Patel also made things worse by having himself run out by an acrobatic de Villiers.
In Image: Royal Challengers Bangalore's Tillakaratne Dilshan, right, and Chris Gayle celebrate the dismissal of a Kochi Tuskers Kerala wicket