A superb second half performance by Didier Agathe was the catalyst for much of Celtic's play, the winger scored one, the others were scored by John Hartson with two, Stephen Pearson and Henrik Larsson.
It was good to see the Chairman of the Motor Neurone Disease Charity being presented with a cheque for £20,000 before the match, a figure which was made by the Celtic supporters.
Celtic were unchanged from the team who won 3-1 at Pittodrie the previous week, which meant John Kennedy kept his place in the starting eleven.
Kilmarnock came out to play the counter attacking game, and Gary McSwegan could have put them ahead with a couple of chances in the first half.
Celtic failed to get going in the opening period, Didier Agathe was pedestrian and Stephen Pearson was not getting enough service on the left hand side.
Celtic needed an early second half goal to avoid any frustration later in the game, and it came through Didier Agathe. Agathe had obviously been instructed to get further forward, and his neat one-two with John Hartson ended in a smashing shot into the roof of the Killie net.
Agathe then returned the favour to the Welshman, setting him up for a header to make it 2-0.
Kilmarnock were now on a damage limitation exercise, but couldn't stop Henrik Larsson making it 3-0 on 76 minutes.
Stephen Pearson got his name on the scoresheet a minute later, after a fine through ball by Neil Lennon put him one on one with the Kilmarnock goalkeeper, and the two Kilmarnock supporters' buses were almost full.
Still, the Killie fans who remained were treated to a fine consolation effort by Erik Skora, who placed a neat chip over the head of Douglas.
Not content with only a three goal cushion, John Hartson headed home his second of the game with only a couple of minutes remaining, after being set up by substitute Shaun Maloney.
Next up are Hearts away in the Scottish Cup, but I certainly cannot see any team beating us at this present time.
Celtic:
Douglas - 7
Varga - 8
Kennedy - 5
McNamara - 8
Lennon - 9
Sutton - 8
Agathe- 8
Petrov - 8
Pearson - 7
Hartson - 7
Larsson - 7
Celtic-Mad Man of the Match: Neil Lennon