For the first time in a decade they have given themselves a clear advantage over their great rivals and, although Hearts are still involved, the feeling is Celtic can now only lose the league.
They are two points ahead of Hearts and have a four-point cushion over Rangers following their 1-0 win over Hibernian on Saturday while their title rivals were drawing 2-2 at Ibrox.
Jorg Albertz fired a lastminute equaliser for Rangers in a game where defensive mistakes led to both the Hearts goals, an indication that the days of the invincible Rangers defence have gone - along with the resolve that has seen them achieve nine league titles.
With nine games remaining and four points to make up they are not out of the race yet, but have been misfiring badly in recent games, leading to a pessimism among their supporters.
They are likely to be without Richard Gough, their captain, for several weeks after he was sent off on Saturday, a red card he has and will continue to vigorously protest against. The defender, clearly angered by his second caution, said after the game: "I want to speak to Walter Smith, the manager, to put together an appeal. TV evidence has been used to find players guilty in the past so surely it can be used to clear people. There wasn't a malicious tackle in the game."
At the bottom of the Premier Division, Hibernian will continue to fight to make up the seven-point gap between themselves and Motherwell and Dunfermline.
The First Division title race appears to be all but over, with Dundee taking an 11 point lead over Falkirk thanks to a 1-0 win over St Mirren.