The Dons will be kicking themselves, though, with the first two goals very much of their own making.
Ash Taylor's poor back-pass led to the opener and Barry Robson was caught in possession for the second, before substitute Erskine sealed matters in the dying moments.
Aberdeen had the better of the opening stages and could have been in front after just nine minutes when Taylor, in for the suspended Russell Anderson, flicked Niall McGinn's cross towards Andrew Considine at the far post, but the defender sent his volley over the crossbar.
But the Dons were undone by their own defensive deficiencies. Temporarily down to 10 men as Robson received treatment for a facial injury, they fell behind after Taylor's pass-back fell well short of Jamie Langfield.
Dow took full advantage, getting to the ball first and forcing it past the Aberdeen goalkeeper at the near post.
It took the home side a while to recover their composure, but two minutes before the break they were just inches from a leveller.
Radoslaw Cierzniak flapped at Robson's cross from the left and the ball dropped to McGinn, who took it on the chest before volleying across the goalkeeper only to see it rebound off the base of the upright.
And it would prove costly as the Arabs doubled their advantage on the stroke of half-time.
Again it was a goal Aberdeen will rue conceding. Robson was caught in possession, allowing Nadir Ciftci to thread a stunning through-ball to Mackay-Steven, who sent a low shot past the static Langfield.
The Dons replaced Robson, who had also taken an ankle knock in the first half, with Adam Rooney at the interval, the former Birmingham City man joining David Goodwillie up front.
And they started the second half on the attack, with Peter Pawlett drawing a foul which saw Paul Paton pick up the first booking of the match, only for McGinn to send the resultant free-kick well over the crossbar.
They came close to pulling a goal back when Goodwillie's cross found Pawlett six yards out, but the well-positioned Townsend blocked. United immediately broke, but Ciftci hit well over when a more composed finish could have put the visitors out of sight.
United brought on Erskine for Stuart Armstrong as they tried to find a foothold in the second half, but it was Aberdeen who continued to press, and another driving run from Pawlett brought the second caution of the match as Keith Watson ended his break illegally.
The pressure was mounting on the United goal, but they could have extended their lead against the run of play as Dow broke through a static Dons defence only to fire wide of Langfield's left-hand upright after 69 minutes.
United were forced into a second change after 74 minutes, with debutant Dutch striker Mario Bilate replacing the stricken Mackay-Steven.
Referee Willie Collum is often at the centre of controversy, but his decision not to award Aberdeen a penalty when Rooney went down under pressure from Cierzniak looked to be the correct call.
As the game entered the final throes, on came Nicky Low for Aberdeen and Charlie Telfer for United, and Low was involved in one final chance for the Pittodrie side.
Cierzniak was again unconvincing as he beat away Low's cross but, with the goal to aim at, Goodwillie headed over the bar.
And, as before, they were punished for their profligacy as United broke, with Bilate setting up fellow substitute Erskine to drill a third goal low into the net with the final kick of the game.