On days like these we see what Celtic might yet become under Tony Mowbray. They attacked with an often carefree ambition, disregarding so much of their caution as though it was needless baggage. But then we also saw a gathering of those weaknesses that still leave the manager's vision incomplete.
Early on, Celtic created chances as though they might come as easily as acts of the imagination. Kilmarnock were left anxious and their afternoon seemed suddenly alarming when Aiden McGeady skipped so innocently past Frazer Wright in the 13th minute that he left the defender on his backside before lashing a rising shot beyond Cameron Bell.
This might have been a heady display by Celtic if they did not leave so many of their chances unfulfilled. A carelessness can gather around the best of their work, so that Scott McDonald failed to reach Georgios Samaras's cross, Paddy McCourt drove wide and McDonald shot straight at the keeper Bell from close range. There is often an over-elaboration to Samaras, as if he is beguiled by the thought of himself as a showman, but he was measured enough to eventually convert a second goal with an emphatic header from Andreas Hinkel's cross on 32 minutes.
"We controlled the game and created numerous chances," said the home manager Mowbray. "And we scored a few goals, which makes it a bit easier for everybody."
Having displayed so much of their capacity to thrill in the opening half-hour, Celtic then became strangely subdued. The home defenders allowed the big Kilmarnock striker Kevin Kyle enough licence to head wide from inside the six-yard box just before the interval, then send three headers over the bar in the second half.
These, though, were only brief acts of retort and the home side restored enough of their intent to add a third before the end, when Hinkel released Niall McGinn through the middle and the winger drove a hefty shot past Bell.
There would have been more goals had Bell and his beleaguered defenders not cleared off the line three times in a flurried late spell of Celtic attacking.