The importance placed by Celtic on what would otherwise have been regarded as a routine trip to Ayrshire was apparent by the strength of their team.

It is this season's great Scottish football anomaly that Celtic have earned progression to the last 16 of the Champions League despite regular troubles in their domestic league.

With Europe now on the back burner until February, it is reasonable to assume Celtic will use the intervening spell to endorse their superiority over the rest of the Scottish Premier League. Their strength of personnel from the outset here illustrated there is no plan to ease off during the forthcoming weeks.

Heading to Rugby Park, Celtic were enduring their worst opening to a domestic campaign for 14 years. That statistic highlighted the trouble Neil Lennon's team have encountered when flitting between high-profile European occasions and SPL outings. It must also be taken in the context of weakness elsewhere; Celtic were still clear at the summit before taking on Kilmarnock.

To their credit, Celtic displayed no hangover from their midweek exertions against Spartak Moscow. Lennon's players were clinical and played some fine football in spells; Celtic's third goal came after they had held on to the ball for one minute and seven seconds. There were 22 passes within that spell, in which every Celtic outfield player touched the ball.

"I thought we were brilliant," Lennon said. "The players showed a great appetite and attitude towards the game, the quality of their passing was of a high standard. It looked like they enjoyed themselves out there. Our third goal epitomised everything that was good about this team. They are full of confidence at the moment. The only disappointment is not to keep a clean sheet."

In Adam Matthews and Scott Brown, Celtic had the two best players on display. Brown's level of performance is especially notable as the captain continues to nurse a hip condition which, it seems, will inevitably result in surgery. Not that Brown is of a mind to discuss that; he walked out of his post-match press conference in a childish, swearing strop when pressed on his fitness.

Kilmarnock were well short of their fluent best but could, at least, point to a crucial moment within a minute of the second half getting underway. At that point, their striker Paul Heffernan delayed far too long on the ball with only Celtic's goalkeeper to beat, thereby allowing Charlie Mulgrew to block his shot. The incident rather summed up Heffernan's afternoon and Kilmarnock's bluntness.

Celtic were already a goal ahead by the time of Heffernan's wastefulness. Matthews cut the ball back for Brown, who provided a rare goal with a low finish beyond Cammy Bell. The Kilmarnock goalkeeper has cause to be disappointed at being beaten so easily at his near post.

Moments after Heffernan's chance, Gary Hooper stung the palms of Bell with a fierce angled drive. It was Joe Ledley who was to extend Celtic's lead after firmly meeting a low pass from Brown.

"I had a £20 bet with both Scott and Joe before the game about them scoring a goal," Lennon said. "So I'm £40 out of pocket. I wanted them to chip in with some goals because they are both capable of it."

Celtic's third goal was a wonderful affair. The substitute Georgios Samaras converted it, by meeting Matthews' cross with his head for his seventh goal of the league season.

Kilmarnock's race was run, with their only consolation a Cillian Sheridan volley from a Jeroen Tesselaar cross in stoppage time.

"Celtic were the better team but not enormously so," said Kenny Shiels. "That's the best, I would say, Celtic have played in a long time. You can see in their body language that they can now concentrate on domestic football."

The Kilmarnock manager added: "We met Celtic at a bad time, I feel."