The teenager's 87th minute left-foot shot, after a one-two with Henrik Larsson, was rough justice on Aberdeen, who seemed set to take their first point from this fortress in six years.
That is the way things are going for a team currently seeking their fourth manager in 18 months and given Aberdeen's current fragility the last thing they needed was to concede an early goal. They held out for just 70 seconds and underlined just why the Aberdeen chairman, Stewart Milne, described them as "complacent" before the game.
Andy Dow allowed himself to be easily dispossessed by Colin Healy and the Celtic teenager romped away before delivering a cross intended for Larsson. The Aberdeen central defender Mark Perry poked the ball away from the Swede but only into the path of Regi Blinker, who thrashed in a left-foot shot.
Aberdeen rarely found enough confidence to escape their own half for almost 20 minutes, the one exception to the rule being Michael Hart's neat move. The teenage midfielder chested the ball down before clipping a volley wide of Jonathan Gould's post.
Celtic were hungry to add to their advantage and Tommy Johnson threatened with a 30-yard shot which was just over, but then Gould preserved Celtic's lead with a wonderful 35th-minute save from Dow.
Aberdeen's situation would have been worse had Johnson not found the side netting instead of the goal just after half-time but Aberdeen restored parity in the 55th minute with a wonderful goal which belied their current poverty. Hart supplied the over-lapping Anderson with a clever pass and the full-back's low cross was swept high into the net by the right boot of Andreas Mayer.
The joy lasted for just five minutes before Celtic forged ahead once more. Larsson's cheeky back-heel fell into the path of Johnson. This time the former Aston Villa player showed poise and accuracy to drill a shot beyond the Aberdeen keeper Tony Warner.
Yet Aberdeen drew level again with just 10 minutes left. Gould spilled Eoin Jess's cross under pressure and Perry pounced to stab the ball into the net. Suddenly things were looking up for the Dons - but they did not see Burchill, who came on in the 75th minute for Johnson, waiting to pull the rug from beneath their feet.Reuse content