A mistake from Dons goalie Derek Soutar gifted the lead to the first division club midway through the first half. Ryan McCann floated a free-kick into the box and the goalie failed to gather it.
The ball broke back to former Dons midfielder Stevie Tosh on the edge of the penalty area and the veteran rifled it into the back of the net with glee.
Queens had the ball into the back of the net for a second time five minutes later, but Paul Burns was flagged offside as he fired home from Stephen Dobbie's pass.
The Donnhamers defence was resolute throughout the opening half-hour, showing why they had yet to concede a goal so far this year in the Scottish Cup.
But the Dons eventually levelled from a set0piece ten minutes before the interval. Barry Nicholson's free-kick was nodded across goal and Andrew Considine rose above Queens skipper Jim Thomson to head home.
Queens were forced into making a change just before the interval when John Stewart replaced the injury Dobbie and it was an excellent surging run from the former Aberdeen man player that set up Paul Burns for the Doonhamers' second goal at the start of the second half.
Stewart exhibited an excellent turn of pace as he raced past Zander Diamond and crossed the ball to Burns, who netted at the second attempt at the back post.
This spurred the Pittodrie outfit into action and they were almost level within 60 seconds, but Chris Maguire's low angled drive was brilliantly touched away by Queens goalie Jamie MacDonald.
However Aberdeen did not have to wait long for their leveller as Nicholson got them back on level terms for the second time minutes later. Lee Miller saw his header from Maguire's cross well blocked by MacDonald, but Nicholson reacted quickly to knock home the rebound.
The frenetic start to the second half continued as the Doonhamers retook the lead within minutes.
The Dons central defence failed to cope with a long ball forward and Sean O'Connor took the ball past Diamond before firing home the third goal.
Once again the lead was short-lived as Considine drew the Dons level after Miller had nodded on a Nicholson cross.
There was, however, an air of inevitability about the fact that the Doonhamers retook the lead for the fourth time minutes later as the match started to resemble a game of basketball.
Once again the Dons defence was caught out and substitute Stewart fired home in acres of space at the back post to seal the final berth.
The Dons had chances to level but they were denied an equaliser by the woodwork on two separate occasions 20 minutes from the end.
Diamond headed off the face of the crossbar and as the rebound fell back to the central defender, he sent a half-volley crashing against an upright.