Shunsuke Nakamura was magnificent for the home team and his hat-trick was just reward for an outstanding afternoon. Scott Brown chipped in with a double with Marc Crosas scoring his first goal for Celtic as well.
To round off a terrible afternoon for the visitors John Potter headed into his own goal for Celtic's seventh.
Earlier Jack Ross was perhaps unlucky to be sent off as the referee judged that his tackle on Scott McDonald denied the Celtic striker a clear goalscoring opportunity. Jan Vennegoor of Hesselink's resultant spot-kick was well saved by keeper Chris Smith.
Celtic's opener arrived when Stephen McManus's pass found Nakamura whose powerful shot appeared to be covered by Smith but the keeper let it slip through his hands and into the net.
Even though Smith denied Celtic from the penalty spot it was not long before the Bhoys added a second with Nakamura sweeping his shot home from the edge of the box.
When Crosas struck a magnificent shot past Saints keeper from 30 yards early in the second half, the match was over as a contest.
Brown added a fourth when he drilled his shot low past the keeper and Nakamura celebrated his hat-trick and Celtic's fifth goal with a trademark free-kick into the top corner.
Brown added a sixth for Celtic before Potter's own goal left St Mirren seven goals down with 14 minutes still remaining.
Somehow they hung on for the last few minutes, but Celtic will certainly be encouraged both by the result and the considerable improvement to their goal difference.