The margin of victory was important far as well as now enjoying a two-point lead in the title race, Celtic have also eaten into Rangers better goal difference.
Welsh striker John Hartson was the biggest factor on that score, ending a five-game barren spell by grabbing a hat-trick to take his season's tally to 27.
While Henrik Larsson has not and may never be replaced, Hartson has certainly smoothed the pain of the Swede's departure.
Livingston meanwhile are struggling at the other end of the SPL, one point behind Dundee United and three behind Dunfereline despite a recent comeback prior to Celtic's visit.
The Bhoys had looked hungry from the start with Craig Bellamy wasting an early chance and Hartson also going close in a period which saw Celtic win six corners.
Former Real Madrid defender Oscar Rubio was then injured while blocking another Hartson effort and while he was having treatment Celtic went ahead thanks to the Welshman.
The flying Bellamy almost made it 2-0 moments before the break, but in the second half Celtic keeper David Marshall was forced to make a crucial save from Jason Dair.
It was only in the closing 15 minutes that Livingston's brave attempt at a fightback was finally ended.
Hartson doubled his team's advantage with a trademark header and then stole the ball from regular penalty taker Alan Thompson to send keeper Roddy McKenzie the wrong way from the spot.
Even after Hartson's treble, Celtic still had something extra up their sleeve with defender Stanislav Varga arriving unmarked at the back post to slot home an injury-time cross from the left foot of Thompson.