The hosts scored when Paul Rutherford fired through a crowded penalty area after Millers goalkeeper Conrad Logan failed to clear Richie Baker's corner with a weak punch.
Adam Boyes nearly doubled Barrow's lead but his effort hit the crossbar shortly afterwards.
Grabban levelled eight minutes from time when he spun in the area and blasted a powerful shot home before he got the winner on 87 minutes, converting a penalty after Paul Smith's handball from Gareth Evans' cross.