Charlie Mulgrew sent Celtic on their way to the Scottish Cup final with the opening goal in a 4-0 victory over his former team as Aberdeen paid the price for Andrew Considine's early red card at Hampden.
Jamie Langfield saved Anthony Stokes' penalty after Considine had been sent off for bringing down Gary Hooper, but the Aberdeen goalkeeper was beaten by Mulgrew's free-kick delivery just after the break.
Joe Ledley, Kris Commons, from the spot, and Shaun Maloney took Celtic's goal tally for the season against Aberdeen to 21 as Neil Lennon's men set up a May 21 final against Motherwell.
Stokes had a good chance in the 13th minute when a long Mark Wilson free-kick saw him race past a sleeping Dons defence but his drive from 12 yards was blocked by Langfield at the expense of a corner, which came to nothing.
However, in the 18th minute, after Considine had been sent off for tripping Hooper in the box, Stokes squandered an even better opportunity from the spot. The Irishman drove his penalty to Langfield's right but the former Dundee keeper got down to block before Aberdeen skipper Zander Diamond forced the rebound behind for a corner which, again, the Dons survived.
The Granite City men were primarily concerned with their defensive duties but had their first chance in the 27th minute when Rob Milsom's floated cross found Chris Maguire 14 yards out but his header lacked the power to trouble Fraser Forster.
And it looked like being a long second half for the Dons as Langfield again had to come to the rescue less than two minutes after the restart. Stokes and Hooper combined brilliantly at the edge of the Aberdeen box but the Englishman's close-range shot was blocked by the Dons keeper.
However, all Langfield's good work was undone in the 49th minute. He looked at fault when Celtic took the lead through Mulgrew. After Milsom was booked for a foul on Beram Kayal 35 yards out, the former Dons defender knocked the free-kick into the box and it evaded everyone and caught Langfield off guard as it sped in at the far post.
In the 56th minute Maguire had the ball in the Celtic net but was ruled offside and a minute later Celtic confirmed their final appearance when Ledley latched onto a Stokes cross to send a shot from 12 yards past Langfield and into the corner of the net.
Aberdeen were down and out. In the 62nd minute defender Derek Young conceded a penalty when he brought down Stokes almost on the byline and this time Commons sent Langfield the wrong way from the spot. Maloney got himself on the scoresheet in the 83rd minute he converted a Wilson pass from almost on the goal-line and the Dons' misery was complete.