The tie was effectively over after only 10 minutes by which time the Hoops were leading through goals by debutant Kris Commons, drafted straight into the Celtic side after finalising his move from Derby on Friday, and defender Charlie Mulgrew.
When stopper Thomas Rogne headed in number three after 21 minutes it looked like Neil Lennon's men could be on the way to replicating the 9-0 home thrashing handed out by the Parkhead side when the two teams met in the SPL in November.
Celtic's on-form striker Anthony Stokes scored from the spot 11 minutes before half-time to add fuel to those fears of the dumb-stricken Dons fans, but the game went flat after the break and a Scott Vernon header gave the scoreline a modicum of respectability.
In the March 20 final, the Hoops will meet the winners of the Rangers versus Motherwell semi-final to be played at the national stadium tomorrow. And on this form they need fear neither.
The Dons had lost 1-0 in the SPL at Parkhead last week with a decent display which had encouraged a good Pittodrie support to travel down from the Granite City, and there was a good atmosphere inside Hampden as both sides set about reaching the first major final of the season.
Celtic, fresh from an impressive 4-0 defeat of Hearts, drove forward with impressive purpose from the start and it soon paid off.
In the sixth minute Aberdeen failed to clear a corner and when the ball fell to Commons just outside the box, he flighted the ball over the head of hapless Dons goalkeeper Jamie Langfield, although the Scotland winger's effort admittedly looked more of a cross than a shot at goal.
It was downhill from then on for the Pittodrie men. In the 10th minute Commons' corner from the right was headed towards goal by Stokes and Mulgrew, playing again in the relatively unfamiliar central defensive role alongside Rogne, rose a yard out to knock the ball into the net.
The Dons looked rattled but moments later, in their first real attack, Vernon beat Celtic goalkeeper Fraser Forster with a drive which struck the outside of the post.
In reality, it was the beginning and end of the Pittodrie side's resistance.
In the 20th minute Stokes had a shot touched onto the bar and again Aberdeen failed to deal with the resultant corner.
And when Mulgrew knocked the ball back into the six-yard box, Rogne headed past Langfield.
It was all too much for some of the Pittodrie fans, who began to boo their own side, as Hoops right back Mark Wilson completed a sweeping Celtic move involving skipper Scott Brown and Gary Hooper by driving just over the bar from the edge of the box.
There was more woe for Aberdeen in the 33rd minute after Celtic were awarded a free-kick 20 yards from goal.
Midfielder Derek Young, standing in the Dons' defensive wall, inexplicably stuck his hand in the air to block Stokes' curling shot giving referee Craig Thomson no option but to point to the spot.
After Young was booked, Stokes sent Langfield the wrong way with the penalty and some Aberdeen scarves began to hit the trackside with more vehement boos following on the half-time whistle.
The second half was a formality although Craig Brown's side at least showed some fight.
In the 58th minute Dons substitute Ryan Jack, on in the first half for Nikola Vujadinovic, sent Chris Maguire through, but although the Pittodrie striker rounded Forster, the angle was too tight and he blazed over.
However, in the 61st minute, after Celtic left-back Emilio Izaguirre earned a booking for a foul on Maguire wide of the penalty area, the Dons pulled a goal back when Rob Milsom's free-kick was met by the head of Vernon 10 yards out.
Celtic were content to see the game out and consequently pushed forward only in bursts, Hooper's drive from the edge of the box 10 minutes from time lacking the belief that had characterised their first-half display.
With four minutes remaining Vernon knocked the ball over the bar from less than six yards out after being set up by Dons substitute Josh Magennis, who had replaced Young, and then he had an attempt cleared off the line by Wilson, but it was all academic.
The game ended with Aberdeen probably happy that their defeat had not been more painful and Celtic content in the knowledge that they are now firing on all cylinders with the business end of the season approaching.