The end of a league season of unprecedented domination could well come Saturday for Martin O'Neill's Celtic side.
Victory at home over bottom club St Mirren will confirm the championship and the second leg of a domestic treble.
Dundee, skilful and energetic, looked set to scupper the timetable last night before Johan Mjallby's 84th-minute winner sealed Celtic's 15th home win in the league.
The visitors' case was hardly helped when their goalkeeper Marco Roccati suffered a back injury while warming up.
His replacement James Langfield was picking the ball out of the net within five minutes.
There was no question what was the most telling feature of Tommy Johnson's goal.
Before moving forward to first-time Henrik Larsson's low cross, he took a step back to suck the defender Steven Tweed a few vital inches out of position, then used the space created to step across his opponent's path.
Celtic's speed of thought threatened to tear the visitors to shreds, but Claudio Caniggia, supposedly interesting both sides of the Old Firm, dragged his team-mates into the game with a display of individual skill that was contagious.
Celtic's safety-first policy in defence contrasted with a more speculative instinct up front, though Johnson seemed unable to follow his goal with further confident touches, snatching at one clear chance with the interval looming.
A slight knock robbed the game of Caniggia's genius at the interval. His replacement was another much-admired Argentine, Fabian Caballero.
Suddenly it was Celtic's turn on the back foot. Except for Didier Agathe's thrilling runs, the balance of play was shifting, one well-constructed move allowing Alberto Garrido to trouble Robert Douglas with a long-range shot.
But Celtic are top because they can hold their nerve when the initiative drifts from them.
This time though, they were tested more than usual when Gavin Rae's delicious ball into the heart of the Celtic defence was met by Juan Sara's equally delicate volley to level the score.
CELTIC: Douglas, Valgaeren, Mjallby, Vega, Agathe, Lambert, Lennon, Moravcik (Boyd 72), Thompson, Johnson (McNamara 62), Larsson. Subs Not Used: Gould, Healy, Crainey. Booked: Lennon. Goals: Johnson 5, Mjallby 84.
DUNDEE: Langfield, Smith, Marrocco, Tweed, Coyne, Artero, Nemsadze, Rae, Garrido (Carranza 58), Sara (Khizanishvili 83), Caniggia (Caballero 46). Subs Not Used: Fatello. Sent Off: Smith (81). Booked: Tweed, Marrocco, Artero. Goals: Sara 67. Attendance: 59,562.
Referee: D McDonald (Scotland).
