The midfielder, who had two spells on loan at the Pittodrie club prior to this season, scored what proved to be the winner with a shot in added time at the end of the first half.
Dons goalkeeper Joe Lewis brilliantly saved Scott Sinclair's controversial penalty in the 52nd minute of a pulsating second half which thrilled until the final whistle.
Since taking charge of the Parkhead club in 2016, boss Brendan Rodgers has won every piece of silverware on offer and this most recent victory - the 18th in the competition for Celtic - is the first step towards a third consecutive domestic treble.
Aberdeen manager Derek McInnes has now lost three cup finals to Celtic during the Hoops' current period of domination which shows no sign of abating, but his side put up a valiant display, if there is any consolation to be had from that.
For Rodgers, he can do no wrong in Scottish football.
He made only one change from the side which started the 1-0 UEFA Europa League win over Rosenborg in Trondheim with deputy keeper Scott Bain taking over from Craig Gordon, as he had done in previous rounds of the competition.
McInnes went with the burly figure of Sam Cosgrove in attack and there was no sign of any Aberdeen reticence in the rough and tumble first half.
Socceroos midfielder Rogic struck the outside of the post in the seventh minute with a left-footed snap-shot from 25 yards before James Forrest's attempt with the outside of his right foot escaped keeper Lewis's right-hand post by a yard.
Bain was tested for the first time in the 16th minute with a close-range shot from Andrew Considine after a corner although the flag was up for offside.
Aberdeen battled for a share of possession and in the 36th minute midfielder Lewis Ferguson headed a Niall McGinn corner over the bar.
Two minutes later Bain saved a header from Gary-Mackay Steven who in the process clattered heads with Dedryck Boyata.
The Hoops defender was able to play on after treatment but the former Celt, after a lengthy spell of attention from the medical staff, was taken from the field on a stretcher to an ovation from both sets of supporters, to be replaced by Connor McLennan.
There were six added minutes at the end of the first half and just before they came to an end Celtic went ahead.
Christie raced on to a long pass from Boyata, forced his way past Dons captain Graeme Shinnie and with Shay Logan and Scott McKenna also in the vicinity, he slammed the ball high into the net, after his first shot had been parried by Lewis.
There was drama seven minutes after the break when Dons midfielder Dominic Ball was judged by referee Andrew Dallas to have handled a Christie pass inside the box.
It looked not only accidental but outside the penalty area - but Lewis threw himself to his right to push Sinclair's penalty behind for a corner which was defended by the Pittrodrie side who recognised they had been given a lifeline.
Lewis then saved a powerful drive from Celtic defender Filip Benkovic and again the Dons held firm at the corner.
Defender Jozo Simunovic replaced Boyata on the hour-mark and immediately his attempted clearance smacked off his own crossbar.
Scott Brown came on for Rogic and the all-action match continued apace.
McKenna flashed a header across the Celtic six-yard box before Lewis saved two Odsonne Edouard attempts.
However, Aberdeen ran out of time before Celtic fans celebrated another trophy win with more promised before the end of the season.
