The Bhoys took their time to find their rhythm and as the match began it looked as if their gruelling European tie four days earlier would take its toll on their performance. St Mirren in contrast looked bright and well-organised.
But fears of a European hangover were dispelled when the match changed midway through the first half when Scott McDonald stormed through the middle of the park, beating three defenders and threaded the ball through to Scott Brown, who clipped the ball under goalkeeper Chris Smith.
On 25 minutes, less than three minutes after the first goal, Celtic struck again as McDonald beat goalkeeper Smith, chipping the ball over his head from 18 yards out after he had come off his line.
Things went from bad to worse for St Mirren in the second half and Celtic continued their push for victory.
On 53 minutes Derek Riordan whipped a corner into the box and Jan Vennegoor of Hesselink rose above the hapless Buddies defence to head into the net unchallenged.
At the other end Arthur Boruc, following his penalty heroics on Wednesday night, was left with nothing to do but watch his team-mates.
The visitors could have sat back and defended their lead at this point but they continued to drive forward in numbers and Riordan helped make it 4-0 on 56 minutes, as his effort took a deflection off Franco Miranda and beat Smith.
Former Hibs man Riordan was nearly on target after 74 minutes but saw his effort blocked. However, the Saints defence failed to clear the ball and after a goalmouth scramble, Hoops captain Stephen McManus drove the ball in from four yards to complete the rout.
Miranda gained revenge 15 minutes from time with a magnificent right-footed strike to earn a consolation goal for St Mirren, but it will have come as little comfort to manager Gus MacPherson, who will be left wondering what he can do to bolster his leaky defence.
Gordon Strachan's men remain just two points behind their Old Firm rivals with an almost identical goal difference and the season is shaping up to be another epic battle between the two Glasgow giants.