Killie manager Jim Jefferies welcomed Alan Combe back into goal after a groin injury, and he named an attacking line-up with Danny Invincibile and Willie Gibson playing as orthodox wingers.
Celtic boss Gordon Strachan waited until he walked on the surface before naming his side and felt confident enough in the surface to start with his most skilful midfield including Shunsuke Nakamura and Aiden McGeady, and also named new signing Georgios Samaras among the substitutes.
After a quiet opening, Celtic stepped on the accelerator in the second quarter.
They began wave after wave of attacks with first Nakamura freeing Jan Vennegoor of Hesselink to square for Scott McDonald on the six-yard line, only for the Aussie striker to be denied by an excellent Simon Ford tackle.
McDonald was denied again a minute later by a smart Combe double save, but it was third time lucky in the 22nd minute when he popped up at the near post to stab home Paul Caddis' cross.
Despite being battered for long spells, Kilmarnock could have gone in level at half-time.
In the 36th minute, Artur Boruc looked uncertain as he pushed Martyn Corrigan's 25-yarder round the post and two minutes before the interval, Gary Wales was tantalisingly close to Gibson's driven cross with the defence beaten.
The tie looked to be effectively over seven minutes after the break when Gary Caldwell rose highest to meet Nakamura's flicked-on corner to head home number two for Celtic.
Number three followed in the 58th minute on a Celtic break after Killie substitute David Fernandez gifted possession to McGeady, who quickly played in Vennegoor of Hesselink and he smashed the ball past the helpless Combe.
Killie clawed one back when Jamie Hamill headed Invincibile's cross past Boruc in the 65th minute.
But any thoughts of a comeback were quashed within a minute when McDonald swept home his second after another Combe parry.
It was his last act as he was immediately replaced by debutant Samaras.
And the Greek striker gave a glimpse of his ability in the 85th minute as he glided smoothly past the Killie defence and calmly stroked the ball out of the reach of the keeper and into the far corner for the fifth goal of the afternoon.