Fraser Forster had not conceded a goal since the 3-1 win over the Dons on November 23, but two goals in five minutes - the first a spectacular strike from Jonny Hayes - set the hosts on the way to a 2-1 victory after Virgil van Dijk's early dismissal.
Van Dijk was shown a straight red card for tripping Peter Pawlett in the 13th minute with the home striker through on goal.
Celtic's 10 men held out until four minutes before half-time, when Hayes finally breached the Hoops defence in some style, and Adam Rooney headed a second moments before the interval.
James Forrest pulled one back just after the hour, but Aberdeen held firm to provide Derek McInnes with the perfect response to the disappointing weekend defeat to Partick Thistle.
Neil Lennon's side looked the more dangerous early on, with Charlie Mulgrew forcing a sharp low save from Jamie Langfield and Anthony Stokes curling a free-kick over the bar.
But the game changed when Van Dijk was sent for an early shower, and Niall McGinn - the last person to beat Forster in league action - almost opened the scoring when dragging a shot inches wide.
A last-ditch clearance from Adam Matthews denied Mark Reynolds a close-range shot, and Rooney was agonisingly close to connecting with a driven cross from Hayes.
Nit Biton tested Langfield as Celtic countered before Hayes broke the deadlock with a ferocious 25-yard piledriver that moved significantly in the air and flew past Forster into the top corner.
It went from bad to worse for the visitors on the stroke of half-time when a pinpoint cross picked out Rooney to nod past Forster from close range and send Aberdeen into the break 2-0 up.
Celtic bravely rallied after the interval and pulled one back moments after having penalty appeals waved away, substitute Forrest sweeping Scott Brown's pass beyond Langfield.
Barry Robson's low drive was too close to Forster as the Dons responded, while Stokes fired well wide at the other end before the Celtic striker hit the target but Langfield was in the way.
Georgios Samaras and Mulgrew both had late shots charged down as Celtic fought to extend their unbeaten league run to 30 games.
But they were blunted by staunch defending from their closest rivals, who should have added a third in the dying seconds when McGinn raced clear but overhit his pass to an unmarked Pawlett.