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The resilient Dons restricted Derek McInnes’s side to one shot on target in a low-quality first half, but the Ibrox side picked up the pace after the break.
Stephen Robinson’s side survived relentless pressure at times but in the 83rd minute, the big striker redirected a strike from James Penrice into the net for his eight goal of the season which settled the semi-final at Barclays Hampden.
Rangers will face Hearts or Hibernian in the December 13 final, with the Edinburgh sides facing each other at the national stadium on Sunday.