You could almost hear the champagne corks being popped on the green side of Glasgow from the fourth minute at Firhill as Anthony Stokes headed home Emilio Izaguirre's cross.
Refusing the lie down without a fight, the home side responded impressively and caused problems for the remainder of the half.
Yet they had no answer just after the break when 17-year-old Liam Henderson grabbed his first professional goal, coolly converting after collecting a cross.
With the song 'championees' reverberating around the ground, Celtic began to really assert their dominance, Stefan Johansen rifling home a third.
Christie Elliot turned the tide a little with an 85th-minute goal, only for Neil Lennon's men to put an emphatic stamp on the game courtesy of late goals from Stokes and Kris Commons.
In the evening's other game, Dundee United put breathing room between themselves and Inverness Caledonian Thistle with a 2-1 win.
In a meeting of fourth versus fifth, United were put on their way when Ryan Gauld finished off a fine move.
A fortuitous second came after the break, goalkeeper Dean Brill's clearance hitting Ryan Dow and finding the net.
Liam Polworth's screamer offered Inverness hope, but United clung on to leave themselves five points ahead of their opponents and just four off the UEFA Europa League spots.
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