Charlie Mulgrew sent them on their way with the opening goal against 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.
Source: PA
Source: PA