Chances flowed. Kyogo got in but was off target. Reo Hatate blazed over from six yards. Kyogo then squared for Kuhn to tap home but Robbie Deas got there.
As half-time approached, things changed dramatically.
Derek McInnes' side showed real bravery to press, commit numbers forward and go man-for-man at the back.
It paid off when Murray crossed, the ball hit Deas' hand and fell to Bobby Wales, who scored. After a VAR check, it was given.
Kilmarnock's belief became palpable as they continued that approach.
It did leave a lot of space to be exploited, though, and eventually it was. Maeda broke free but as he scampered away Lewis Mayo showed pace to deny the winger.
McInnes celebrated that like a goal but moments later Maeda delivered, again wide open from Kuhn's run across the box, and he finished coolly.
Celtic upped it from there. Kuhn smashed off the bar, Hatate was superbly denied by O'Hara and Kuhn then missed from eight yards, but the holders had done enough to progress to the next round.