The home side made heavy work of their win on a Pittodrie pitch showing the scars of a hard winter, and they even had to play for the last 15 minutes with only 10 men, Isaac Osbourne going off injured after manager Craig Brown had made his third substitution.
Right from the off, Aberdeen were determined to attack a young and inexperienced Dundee central defence. As early as the third minute, a Johnny Hayes cross found Vernon at the back post, and although his close-range strike seemed to come off the arm of Gary Irvine, referee Brian Colvin was unmoved by the appeals for a penalty.
Ten minutes later, Dundee went close through Brian Easton, whose low shot was pushed away by Jamie Langfield. The Dons eventually scrambled clear as John Baird tried to pick out Lewis Toshney.
But after 18 minutes, Aberdeen took the lead, and a fine goal it was. McGinn picked up the ball on the halfway line and shuffled past two men before unleashing a low, 20-yard drive which bounced just in front of Rab Douglas, and nestled in the back of the net.
It was a full 20 minutes before the next real chance for either side. Douglas punched away a Hayes cross and Osbourne set himself for a strike from the edge of the area, but sliced his right-footed effort well wide of the upright.
A minute before the interval, the visitors were within inches of an equaliser. Gary Harkins played in Jim McAlister, and the former Morton man cannoned a shot past Langfield, off the underside of the crossbar and back out.
The Dees started the second half brightly and, six minutes in, McAlister tried a low shot from the edge of the area, which Langfield did well to push round the post.
Aberdeen made the first move from the bench just after the hour, with Naysmith replacing Clark Robertson, but a minute either side of the change, Dundee had half-chances for Baird and Riley, though neither really connected with their shot, and former Dark Blue Langfield remained untested.
The Dons switched Rob Milsom for Peter Pawlett with 25 minutes left, and five minutes later they had a brief glimpse of goal as McGinn flicked a shot across the face of goal with the outside of his right foot.
The third and final change for the home side saw Josh Magennis replace Joe Shaughnessy, much to the chagrin of the home support, and they cruelly lost Osbourne to injury just a minute later, reducing them to 10 men.
Dundee were making a decent attempt to find a way back into the game even before Osbourne went off, and they quickly brought on Nish for Conroy in a bid to make the most of their man advantage, but it was not to be for Barry Smith's men.