The game went through the motions in the opening stages at Celtic Park, as neither team was able to assert any immediate dominance.
A few tentative chances began coming the way of the Scottish champions, as Stefan Johansen was denied by Shaleum Logan in the eighth minute, while Emilio Izaguirre's effort was scooped up by Jamie Langfield.
As the game went on, Celtic began cranking up the pressure as they became more and more determined to break the deadlock. In the 25th minute they succeeded in getting on the scoresheet, as Brown cut inside and curled a shot past the Dons goalkeeper.
However, the away side equalised just three minutes later, courtesy of a defensive mistake by the Bhoys. Adam Matthews's back pass was unable to reach Fraser Forster, and Niall McGinn duly took advantage to whip the ball past the beleaguered goalkeeper.
The Celtic captain ensured that the Scottish champions would go in at the break a goal up with just a minute to go in the half, thanks to his low shot which beat Langfield after some good work by Matthews.