Then again, after winning on only one of their previous six visits, any victory would have been welcome for the Dons.
Hamilton won both fixtures at the Superseal Stadium last season but Derek McInnes’s side had won seven of the last 10 meetings between the clubs, which might explain why fewer than 1,000 home fans turned up for this latest instalment.
Hamilton were eager to improve a poor record in this competition (they reached the last eight only once in the previous nine seasons, losing to last night’s opponents) and forced a succession of early corners as the visitors adjusted to the artificial turf.
It was the Dons who created the first half-chance in the 11th minute, with Shay Logan setting up Nicky Maynard for a shot which should have troubled Gary Woods but didn’t.
Darian MacKinnon then picked up a caution for a foul on Kenny McLean on the edge of the 18-yard box but the midfielder’s effort from the resulting free-kick was smashed into the wall.
However, Accies threatened on the break and goalkeeper Joe Lewis required treatment after saving bravely at the feet of Steven Boyd as they both tried to reach Ali Crawford’s through ball.
Ryan Christie had an opportunity to break the deadlock midway through the first half, swivelling on a McLean cross to fire just wide of Woods’ left-hand post.
The on-loan Celtic midfielder spurned a gilt-edged opening shortly afterwards. Woods miskicked a clearance to Maynard, who squared the ball to Christie only for him to miss the target from six yards.
As Aberdeen ramped up the pressure, full-back Andy Considine drove a McLean corner into the ground and Woods did well to fist it clear before diving to his left to keep out a long-range attempt from Graeme Shinnie.
Hamilton were under the cosh but the visitors were making hard work of finding something to show for all their possession.
French defender Xavier Tomas, ordered off in Saturday’s opening Premiership fixture between the clubs, collected a third yellow card in five days when he took out Christie just inside the Hamilton half.
The goal Aberdeen had been threatening finally arrived just before the break. Scott Wright laid the ball off for Shinnie, whose shot ricocheted off a defender and into the path of McLean, whose right-foot drive beat Woods low to his right.
Even then, Lewis was at full stretch to fingertip away a full-blooded drive from Greg Docherty in first-half stoppage time.
It would have been ludicrous if Aberdeen had found themselves level again before reaching the dressing room but the lack of a cutting edge could be their downfall this season.
Accies broke again in the 52nd minute, with Steven Boyd releasing Rakish Bingham. The Englishman took too long to pull the trigger, though, and Mark Reynolds got back to block his shot.
Tomas then headed narrowly wide from the resulting corner, as if to underline the precariousness of Aberdeen’s lead.
Docherty appealed for a penalty, more in hope than expectation, when he and Anthony O’Connor tangled inside the area. Referee Nick Walsh was right to dismiss the claim.
Shinnie tested Woods with an effort from distance but that was an isolated occurrence; Aberdeen had abandoned the passing and moving which had proved so potent earlier on.
Last season’s beaten finalists seemed content to hold on to what they had, an injudicious tactic at the best of times, never mind in knock-out competitions where the lottery of a penalty shootout always looms.
Greg Stewart ought to have sealed the outcome when fellow substitute Miles Storey picked him out with a cross but, under no pressure, the on-loan Birmingham City midfielder skied his shot from the corner of the six-yard box.
That wastefulness almost cost them in the dying minutes when Crawford was inches away with a low drive from the edge of the penalty area.