The visitors were disappointed their efforts and a dominant second half did not bring reward, though Barry Smith, their manager, was as buoyed as he could be in the circumstances, by determined show from his side.
"I can't fault my players and we won't give up on our aim to remain in this division," he said. "We took charge of the second-half of the game and deserved something for our efforts."
For the home supporters, the principal topic of discussion in the build-up to this game was the unthinkable possibility that they would not record a win. After all, weren't they detached at the bottom of the league table and facing relegation? Hadn't they leaked an astonishing 45 goals this term, 22 on the road?
Those statistics may, indeed, be accurate, but Dundee were fully aware that their opponents were no world-beaters and that they had failed to win in their last six starts and had recorded just three home wins this season. They would have been right to have believed they had a chance of creating a shock.
Such an assessment is, according to Craig Brown, the Aberdeen manager in his programme notes, a "glass half-empty attitude here in this neck of the woods which is unique in my experience in football".
A slap on the wrist for disgruntled members of the Red Army? Or chastisement for those members of the media who have questioned whether he has a future at Pittodrie? Perhaps both.
Despite weathering an initial storm as Aberdeen sought a quick goal and referee Brian Colvin waved away claims that Gary Irvine had handled a Scott Vernon shot in the area, the visitors were no shrinking violets and Gary Harkins hit a dangerous strike from distance which forced Jamie Langfield into acrobatic action to turn the ball around the post.
Aberdeen have relied heavily on McGinn, their Northern Ireland internationalist, to bring them goals this season and the striker duly provided the only statistic that truly matterd on the night with a delicious 25-yard shot in the 18th minute. As the ball sailed into the net of Rab Douglas, the Dundee goalkeeper, there were expectations that the floodgates had been pushed open.
With a heavy pitch and a high tempo, play raged from end to end; Nicky Riley's impressive pace and trickery was exciting to watch as Dundee tried to remain in touch and when Harkins and Jim McAlister linked-up just before the break, the latter cracked a close-range shot off the underside of the Aberdeen bar with Langfield beaten.
It was a manoeuvre that, while offering the visitors a crumb of comfort as they headed for their half-time cuppa, had Brown questioning a hesitant defence which was without the centre-back Mark Reynolds, unavailable because of suspension.
He was right to be apprehensive, especially with Joe Shaughnessy, deputising in central defence, looking so uncomfortable when put on the back foot and when McAlister tried his luck from 20 yards five minutes into the second half, Langfield's agility once more came to Aberdeen's rescue and Smith urged on his players from the technical area as Brown looked perturbed that his defence was being breached too easily. Just after the hour, he replaced Clark Robertson, struggling against Riley, with Gary Naysmith for his first appearance for more than three months, since when he has been recovering from injury.
But with 15 minutes remaining, and having used all three substitutes, Aberdeen were handicapped when Isaac Osbourne pulled-up with a hamstring injury and was forced to limp off leaving them a man down and facing an anxious finish.
"Our second half performance wasn't good," Brown said. "Dundee were better in that period and put us under a great deal of pressure. It was difficult in the end playing with 10 men because of Osbourne's injury, but we got through it.
"Mind you, the hand ball by Irvine in the opening minutes was a clear penalty which, had it been awarded and scored from it, would have made us more comfortable.
"The three points will kick-start the remainder of the season for us. That Dundee team should not be isolated at the bottom. I am in no doubt they will take points off teams between now and the end of the season."