Goals from Henrik Larsson, Stan Varga, an own goal by Phil Stamp and a brace from Liam Miller sent the Hearts support home to Edinburgh with 40 minutes of the game remaining.
In truth it could have been 6 or 7 if Celtic felt in the mood, but the Hoops seemed to take their foot off the gas, in preperation for Tuesday's game in Brussells.
The Celtic crowd played a big part in the early stages of the game, getting right behind the team from the first whistle. Hearts' tactics seemed to be to have a go and kick every Celtic player off the park.
With Henrik Larsson already curling a shot off the bar, Celtic's superiority was rewarded after 9 minutes, when Liam Miller reacted to a Larsson shot which was parried away by Hearts' goalkeeper.
A Stan Varga throw-in was flicked across goal by John Hartson three minutes later, and Hearts midfielder Phil Stamp panicked - heading the ball into his own net, leaving Hearts stunned.
The game was finished before half time, Larsson latched onto a Varga header, when through on goal he cooly slotted past the Hearts' 'keeper.
Stanislav Varga got his first Celtic goal with a few minutes of the half remaining, smashing home a header from a Petrov corner.
With memories of last season - Hearts fans celebrating as if they had won the European Cup after beating Celtic at home, it was a joy to send the Hearts fans home at half time!
Shaun Maloney replaced Stan Petrov at half time and immediatley set out to impress boss Martin O'Neill.
It didn't take long for Celtic to grab a fifth and final goal, Liam Miller got it. Shaun Maloney's superb corner was put back across goal by John Hartson and the young Irishman was there to smash home.
From then on, it was played out like a training match - and was a truly fine performance by the Bhoys.
Today was a great result and has set us up fine for Anderlecht on Tuesday. Bordeaux, meanwhile, must be shaking in their shoes!
Celtic:
Hedman - 7
McNamara - 7
Varga - 8 (Kennedy - 7)
Balde - 8
Lennon - 9
Thompson - 7 (Gray - 7)
Petrov - 7 (Maloney - 8)
Agathe - 7
Miller - 9
Larsson - 9
Hartson - 8
Celtic-Mad Man of the Match: Liam Miller