After being under pressure for most of the game, with their first attempt on goal after the break Mackie fired past Artur Boruc from 12 yards out.

Celtic had equalised late into injury time in the first game but this time the Dons held firm to set up a semi-final meeting with Queen of the South on the weekend of April 12/13.

But Dons manager Jimmy Calderwood will wonder how his side managed to leave Parkhead with their goal intact while Celtic boss Gordon Strachan will reflect on the jeers of the Hoops fans at the final whistle.

The 60,000-capacity stadium was less than full at kick-off but those inside witnessed Massimo Donati drive over from 30 yards with less than a minute gone as a one-sided first half began.

Moments later, Jan Vennegoor of Hesselink headed a Lee Naylor cross over the bar from eight yards out after good work by Aiden McGeady on the left.

While the home fans sat back and waited for the opener, the small band of Aberdeen supporters gave their side terrific backing as their side held out with increasing confidence.

However, in the 17th minute Dons midfielder Karim Touzani had to react quickly inside his own box to block Shunsuke Nakamura's drive after Hoops striker Scott McDonald had skipped free on the right.

Moments later Vennegoor of Hesselink stretched to volley Nakamura's cross over the bar from only six yards out and with it, the best chance of the first half was gone.

In the 29th minute Dons defender Alexander Diamond appeared to handle the ball inside the Pittodrie penalty area in an aerial duel with Vennegoor of Hesselink but referee Charlie Richmond kept his whistle silent, as he did seconds later when McDonald tumbled theatrically inside the box after clashing with the same player.

In the 38th minute McDonald should have scored when he was set up by Vennegoor of Hesselink 14 yards from goal but the Australian international perhaps tried to be too precise as he curled his shot just past the far post.

The Hoops, however, were almost caught out seconds before the interval.

Aberdeen midfielder Richard Foster latched onto a slack pass-back by Stephen McManus but Boruc was quick off his line to save a rather hurried attempt and spare the blushes of his skipper.

Touzani was replaced by Sone Aluko at the interval but initially it did little to disrupt the pattern of the match.

Celtic piled forward again, McGeady cutting inside in the 50th minute to deliver a tame shot from 25 yards that Soutar gathered easily.

Dons full-back Alan Maybury plucked up the courage to try his luck from 30 yards as the Parkhead defence back-tracked but the ball sailed high and wide.

In the 58th minute Diamond went off after taking a bang in the face from Vennegoor of Hesselink and while he was receiving attention at the side of the pitch, McGeady carelessly fired a volley wide from 16 yards.

The Dons defender failed to return and was replaced by Lee Mair but Celtic continued their procession towards Soutar with Donati driving a couple of yards over the bar from distance.

But in the 69th minute the Dons dramatically stole the lead with their first attempt on goal of the second half.

After a rare spell of pressure Celtic failed to clear their lines and, in a busy penalty area, Dons striker Lee Miller flicked the ball through to the unmarked Mackie, who rifled the ball past Boruc from about 12 yards out.

In the 74th minute Georgios Samaras replaced McDonald as the tension inside Parkhead increased and seconds later Soutar flew to his left to save a trademark Nakamura free-kick from distance.

Vennegoor of Hesselink's goal-bound header hit the head of Andrew Considine before going over for the first of several more corners, which the Dons somehow survived.

In a tense last few minutes Soutar fumbled a close-range shot by Samaras but escaped and substitute Derek Riordan, on for Gary Caldwell, volleyed over from five yards out while even Boruc had an attempt that cleared the bar.