The Russia striker twice slotted home after being played in by Niko Kranjcar as the Premier League side led 2-0 at the interval, though their League One opponents could have been level at that stage as Jay O'Shea missed a good chance and Sam Baldock hit the post.
But Luke Chadwick curled home a superb 25-yard strike to cut the deficit and Jabo Ibehre touched home Daniel Powell's shot to equalise.
Harry Kane replaced Jermain Defoe and scored twice, either side of a stunning 35-yard dipping volley from stand-out performer Kranjcar, while Ibehre added his second and the Dons' third.