Jamie Langfield saved Anthony Stokes' second-minute penalty after Andrew Considine's red-card offence, but the Hoops were not to be stopped for long.
Gary Hooper broke the deadlock after 12 minutes before Mark Wilson and Stokes scored in three second-half minutes to put it beyond doubt.
Mexican international Efrain Juarez replaced the injured Thomas Rogne in Celtic's only change from the side that eased to victory in the Co-operative Insurance Cup semi-final on Saturday.
Celtic boss Neil Lennon failed in his attempts to land central defenders Abdoulaye Faye and Kelvin Wilson before the transfer window shut on Monday night and was forced to field full-backs Wilson and Charlie Mulgrew at the heart of his defence once again.
Aberdeen, eager to avenge their 4-1 reverse at Hampden, made two changes with striker Nick Blackman and midfielder Ryan Jack both handed starts with Derek Young dropping to the bench and Nikola Vujadinovic missing out due to injury.
Steven Smith, who completed a transfer deadline day loan move from Norwich on Monday, was handed a place on the Aberdeen bench as was recent recruit Myles Anderson.
The game got off to an explosive start when Celtic were awarded a penalty in the opening minute, Considine was adjudged to have fouled the advancing Brown.
The Dons defender was shown a straight red card but Aberdeen goalkeeper Langfield guessed correctly to keep out Stokes' penalty.
However the inevitable opener for the visitors came after 12 minutes when Hooper exchanged passes with Stokes before calmly slotting the ball past the despairing Langfield.
Things went from bad to worse for the Dons as they were forced to make two early changes with Young coming on for Jack after only 17 minutes and Smith handed an early debut in place of the injured David McNamee a minute later.
Substitute Young was struggling to deal with the pace of Kris Commons and picked up a yellow card for a foul on the former Derby winger after 30 minutes.
Scotland international Commons drew a fine save from Langfield soon after, before Robert Milsom cleared Hooper's close-range effort off the line as the Celtic onslaught continued.
Biram Kayal was inches away from doubling Celtic's advantage when his powerful left-footed drive smashed off the post to safety.
The Dons had chances to equalise before the half ended with Blackman firing just wide and Celtic stopper Fraser Forster making a smart save to deny Chris Maguire.
Aberdeen skipper Paul Hartley picked up an early yellow card for dissent before Commons spurned an excellent opportunity to add a second for the Celts when he waited too long to pull the trigger after strong running by Hooper.
Aberdeen's Scott Vernon, deployed as a right midfielder following the early dismissal of Considine, picked up a booking for a crude tackle on the lively Commons just before the hour mark.
Maguire, starved of service for much of the match, joined him in the book for a challenge on Wilson soon after as the home side's frustrations grew.
Commons missed another glorious chance to put the game beyond doubt when he outsprinted Smith before rounding Langfield but managed to hit the post from an acute angle when it looked easier to score.
However the decisive second goal came with 15 minutes remaining when Wilson reacted quickest to powerfully head home Commons' near-post corner.
And Stokes added a third for the Celts when he picked up Hooper's lay-off and drilled a left-foot strike past the helpless Langfield after 78 minutes to the delight of the vocal travelling support.