An enjoyable encounter kicked into life early when the Bairns almost took the lead after only 45 seconds.
Anthony Stokes fired in a low right-foot shot from the edge of the box that forced Jamie Langfield to dive full stretch and turned round the post.
It was the home side again who came close with nine minutes played but Darren Barr's header smashed off the crossbar and bounced to safety.
That was as much goalmouth action as the crowd witnessed in the first half, as some tactical tinkering saw Scott Severin move from midfield to the back, stifling the entertainment.
Ten minutes after the re-start Aberdeen took the lead with a quality goal.
Barry Nicholson's corner was headed out to Gary Dempsey 24 yards out and the midfielder sent a screaming right-foot shot low inside Scott Higgins' left corner.
Stokes was unlucky not to level things when his looping cross-cum-shot in the 73rd minute rattled off the junction of crossbar and upright but, with nine minutes remaining, the Dons made sure with a second.
Stephen O'Donnell and Barr barged into each other as the last line of defence and the visitor's sub, Dyron Daal, found himself free to slot past Higgins.