Ben Brannan (far right) put Killie in front after 39 minutes
Kilmarnock won Stuart Kettlewell's first competitive game in charge against Highland League opponents Brora Rangers in the Premier Sports Cup group stage.
Ben Brannan scored the first goal of the Kettlewell era, a right-foot shot from the left side inside the box.
The visitors sealed the three points in Group H with 10 minutes to play, Djenairo Daniels converting from Marley Watkins' set-up.
In Saturday's other group fixture, Livingston won 2-1 away to East Fife.
Livi visit Kilmarnock's Rugby Park on Wednesday (19:45 BST).
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