Kumble, who introduced himself in the seventh over, got his first wicket in the 12th over in the form of Narsingh Deonarine (13) who holed out to Ross Taylor at deep midwicket.
Royston Crandon (5) fell in the 14th over while promising youngster Jonathan Foo disappointed as he fell in the 16th over for just one to Kallis from the six balls he faced and with that Guyana's hopes of a respectable total evaporated.
But for a fighting 30 from Barnwell, who fell in the last ball of their innings, Guyana would not have crossed the 100-mark.
Image: Guyana's batsman Christopher Barnwell, right, plays a shot with Bangalore Royals' wicketkeeper Robin Uthappa at left, during the Champions League Twenty20 cricket match at the Supersport Park in Pretoria
Scores | Champions League