Springbok player ratings in 45-12 win against Wales in Cardiff
Frenchman Dembele headed the defending champions ahead on 37 minutes at Pittodrie before triggering a late counter-attack that resulted in Kieran Tierney sealing the victory.
Celtic crashed out of the last 32 of the Europa League in midweek following a 3-1 aggregate defeat by Zenit St Petersburg but showed their domestic quality against an Aberdeen side that has now lost back-to-back matches.
“It was brilliant win for us 72 hours after the game in Russia at, arguably, one the most difficult places to come,” Celtic boss Brendan Rodgers told the BBC.
“Moussa (Dembele) is a big game player and we are at the stage of the season where he comes alive in terms of what the team needs from him.”
Scott Sinclair and Tom Rogic returned to the starting line-up for the Hoops, but it was Aberdeen who nearly struck first when Kari Arnason was inches away from connecting with a Kenny McLean free-kick.
Celtic then began to assert their authority with Sinclair hitting the crossbar from a corner in the 16th minute, before Rogic was denied by a save at point-blank range from Freddie Woodman.
Aberdeen escaped again when Olivier Ntcham drilled a 25-yard effort against the upright, but the hosts fell behind with half-time approaching as James Forrest crossed for Dembele to nod in for his 10th goal of the campaign.
The Dons threatened an equaliser in the 73rd minute when Dorus de Vries parried a McLean drive, with follow-up efforts from Niall McGinn and Anthony Connor blocked by Celtic defenders.
The visitors were forced to play out the final 15 minutes with 10 men following the dismissal of Mikael Lustig for a second yellow card, but Aberdeen were punished on the break while chasing a way back into the game.
Dembele raced forward from inside his own half before slotting through a precision pass to Tierney to slam home from the edge of the area and ensure Celtic stayed nine points clear of old rivals Rivals, with Aberdeen — who had Sam Cosgrove sent off late on — now 12 points adrift.
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