And when Miller was blocked off by left-back Andy Dawson, Hull suffered a blow as the left-back picked up an injury that saw him replaced by Samuel Ricketts after only 10 minutes.
Celtic's chances appeared to take a further blow after 40 minutes, when Kennedy - not long back from serious injury - was stretchered off, with Steven Pressley making his first appearance of the season following back surgery.
The Blues' preparations had suffered a blow as the late withdrawal of full-back Ben Blair with a hamstring injury prompted a reorganisation of their back line.