The Dons dominated large periods of the game but were largely kept at bay by a visiting side that set out to stifle rather than attack their hosts.
Aberdeen shuffled their pack following the 1-0 defeat to Motherwell, welcoming Mark Reynolds back into the fold in place of Russell Anderson, and Low came into the side for Barry Robson.
County employed Marc Klok to counteract the threat of Peter Pawlett in behind Scott Vernon, one of four changes to the side that had lost 2-0 to Hibernian. Steven Saunders, Alex Cooper and Orhan Mustafi also came in.
The Dons were on the front foot from the off, and had taken the lead within two minutes. Vernon was sent crashing to the ground by Stuart Kettlewell 20 yards from goal, and Low stepped up to curl the free-kick past Michael Fraser at the near post, the ball nicking the post on its way in.
And Derek McInnes' side should have been further ahead 10 minutes later. Pawlett's run into the box was tracked by Klok, but the Dutchman tripped the Dons forward, and referee Calum Murray pointed to the penalty spot.
Vernon stepped up and went high to Fraser's right, but the former Motherwell goalkeeper threw himself across to push the ball around the post.
It seemed only a matter of time before Aberdeen would extend their lead, and only a last-ditch challenge from Ben Gordon denied Vernon after 19 minutes.
Klok had escaped censure for the foul which led to the penalty, but he became the first player booked for a foul on Pawlett in midfield after 25 minutes.
That came around the same time as County began to come into the game, making it a much more even contest, although they still seemed susceptible on the break.
They did have a penalty claim of their own 10 minutes from the interval, although it was perhaps more borne of optimism than anything else, as Alex Cooper's cross was blocked and a shout for handball went up.
Referee Murray was unmoved by the call.
The visitors could have shot themselves in the foot on the stroke of half-time. Niall McGinn danced by Saunders and sent in a low cross which Fraser looked to have covered, only for Scott Boyd to attempt an interception and turn the ball off the outside of his own post.
Mustafi was replaced by Gary Glen at the interval for Derek Adams' men, although the change did little to improve County's attacking threat.
They looked much more capable of coping with their hosts, although Aberdeen remained very much in the ascendancy.
It took almost 20 minutes of the second half before Fraser's goal was threatened, but even then McGinn's swept effort from 20 yards was off target.
County, for whom Cooper was booked for a needless midfield foul, were presented an opening when Michael Hector took the legs away from Klok after 66 minutes, however they failed to take advantage as Graham Carey's struck his 22-yard free-kick into the wall.
County winger Melvin De Leeuw came on for Saunders as the visitors tried to up the ante, while Robson came on for Aberdeen in place of Ryan Jack, who had taken a knock. Cammy Smith also entered the fray, taking over from Pawlett.
County's final change, with 10 minutes remaining, saw Cooper replaced by Darren Maatsen, while Aberdeen's last swap saw Josh Magennis replace Vernon up front.
Still the home side were largely frustrated, but the drive of the 18-year-old Smith at least forced an opening, although his shot was comfortably dealt with by Fraser.
And with two minutes remaining, Boyd's tug on Magennis allowed the ever-dangerous McGinn to send a free-kick wide of the target.