It was the tried and tested striking partnership of Jan Vennegoor of Hesselink and Scott McDonald who netted the vital goals to give the home team a crucial victory in the title race.
Celtic opened strongly and Shunsuke Nakamura should have done better than head wide from Andreas Hinkel's cross.
Aiden McGeady's pass to McDonald was just out of the striker's reach as Celtic probed for an opening goal.
Vennegoor of Hesselink tested Jamie Langfield in the Aberdeen goal with a volley before the visitors at last responded. Derek Young's flick at the near post from Richard Foster's cross was gathered by Artur Boruc.
Jamie Smith's pass found Gary McDonald advancing into the area but Boruc produced a marvellous save to block the midfielder's shot.
Just before the interval Vennegoor of Hesselink's lay-off found Scott McDonald but Langfield saved the striker's shot from 25 yards.
Celtic's opening goal came shortly afterwards as Nakamura's corner was attacked by Glenn Loovens and Gary Caldwell. The loose ball broke to Vennegoor of Hesselink who reacted quickly to prod the ball home from close range.
Aberdeen started the second half on the attack and Chris Maguire out-paced Caldwell only to turn back in the area and lay the ball off to Sone Aluko who shot tamely over.
Caldwell's mistake let Smith in but his pass to Maguire was over-hit. Langfield just beat McDonald to McGeady's cross before Celtic scored their second.
From Vennegoor of Hesselink's clever lay-off McDonald drilled his shot low under Langfield to make the points safe.
The Aussie striker was booked for dissent but nearly added a third with a header from Lee Naylor's cross but Langfield saved well.