The Bhoys gave a debut to new signing Paul Hartley who joined the club during the transfer window while Derek Riordan continued on the left of midfield with Aiden McGeady out injured.
The Glasgow giants must have had an unwelcome flashback to their cup tie with Clyde last season, as Livingston were playing the Bhoys off the park when they opened the scoring in the 18th minute.
A delightfully lofted free-kick from playmaker Lee Makel found right-back Dave MacKay and the former Dundee defender managed to twist in the air to direct his header into the net from 16 yards out.
The shock to the system seemed to stir the beast lying dormant and Celtic began to turn the screw on a Livingston defence that was playing deeper and deeper inside their own half.
A goal was coming and it was the unlikely figure of Darren O'Dea who obliged. The defender found himself stuck in the opposition penalty area after a corner had been cleared, and when Jan Vennegoor of Hesselink flicked the ball into the area, he was in the perfect position to guide the ball into the net.
Celtic looked like they should have been awarded a penalty in the 36th minute when Shunsuke Nakamura was felled in the box by Makel but referee Charlie Richmond seemed oblivious to any crime committed.
The whistler was again at the centre of controversy when Celtic took the lead on the stroke of half-time.
Neil Teggart lay dormant in the centre circle after being scythed from behind but, despite the pleas of several Celtic players to put the ball into touch, the play continued, to the benefit of Riordan who collected Hartley's pass before firing a half-volley into the top corner.
A double salvo on the hour mark effectively killed off any lingering Livi hopes of elevating themselves back into the tie as Riordan grabbed his brace, finishing at the near post after being played through on goal by Nakamura.
Vennegoor of Hesselink continued his fine form in front of goal, as the striker rounded off the scoring for the afternoon when the Lions were still reeling from Celtic's third goal.
It was in fact the former Hibs man who was the provider for the Dutch international, laying the ball off for the former PSV hitman to score with consummate ease.