After the break, the game was more evenly contested with Rangers having the territorial advantage without seriously threatening the home side's lead.
With passions running high, it wasn't a surprise that the opening exchanges were frenetic with both sides cancelling one another out in midfield.
Clever forceful play between Barry Ferguson and Kris Boyd after nine minutes almost created an opening for the striker, but Dons skipper Russell Anderson was alert to the danger and cleared at the expense of his fruitless corner.
Aberdeen opened the scoring on 21 minutes when a long free-kick from Michael Hart wasn't properly cleared.
Jamie Smith cushioned his header down to Scott Severin, whose first-time drive from 30 yards flew high into the net to send the home fans wild with delight.
With Aberdeen's tails up, they again threatened on 28 minutes when Lee Miller's knockdown fell into the path of Steve Lovell, whose crashing effort from 12 yards smashed off the face of the crossbar and away to safety.
Aberdeen finally extended their lead on 32 minutes following more excellent play between Darren Mackie and Lovell.
Mackie's clever pass into the path of his strike partner saw Lovell advance beyond the defence before clipping the ball over the advancing Allan McGregor and into the unguarded net.
Aberdeen had a major let-off when second-half substitute Karim Touzani's mis-timed header from a Charlie Adam free-kick flew just wide of the upright with jamie Langfield stranded.
Anderson almost capped a fine display when his clever turning shot just inside the area was cleared off the line by Alan Hutton with his goalkeeper beaten.
Aberdeen should have had the points wrapped up on 78 minutes when Chris Burke was dispossessed on the edge of his own area by Smith.
His clever ball found Lovell whose weakly-struck shot fell into the arms of McGregor with the goal at his mercy.