An early scare when Magnus Hedman flapped at an easy looking cross was United's only threat of the game, Stan Varga done well to clear the ball off the line.
Henrik Larsson was on fire during the first period, and he linked up brilliantly with Shaun Maloney on 12 minutes for the opener.
Five minutes later the ball seemed to hit off Didier Agathe, for the Frenchman to score his second goal in as many games.
Celtic could easily have scored three or four in the first period, Henrik Larsson forced the United keeper into a magnificent save over the bar.
It was just before half-time when Celtic scored the third. Henrik Larsson was awarded a penalty after being brought down by the goalkeeper in the box, and Alan Thompson placed the ball well to make sure there was no way back for the Arabs.
On 65 minutes, Stan Varga almost took the goalposts apart with a crashing shot from 20 yards out, how the ball did not go in is beyond me.
Captain for the day, Jackie McNamara scored a contender for goal of the season on 67 minutes, and the King of Kings Henrik Larsson added a fifth with only a few minutes remaining.
Celtic played great stuff today, and if we keep up performances like this, no one will beat us.
Celtic:
Hedman - 6
Balde - 7
Valgaeren - 6 (Sylla 68) - 7
Varga - 9
McNamara - 8
Petrov - 8 (Smith 75) - 6
Thompson - 8
Miller - 7
Agathe - 6 (Beattie 74) - 6
Larsson - 8
Maloney - 7
Celtic-Mad Man of the Match: Stanislav Varga