The Juventus striker pounced after 78 minutes following Marko Basa's knockdown from a corner to put his team on 13 points from five games and keep them above England, who travel to meet the group leaders in Podgorica on Tuesday.
Montenegro's hopes of victory in Moldova had looked bleak on the hour when Milorad Pekovic was sent off for a second booking after an uncompromising challenge on Serghei Gheorghiev.
Vucinic and Fiorentina talisman Stevan Jovetic had half chances early on for Montenegro but it was the hosts who arguably should have been ahead at the break.
Alexandru Gatcan and Alexandru Dedov missed decent opportunities with the latter being denied by Mladen Bozovic after the goalkeeper had spilled his initial shot.
Dedov was again dangerous in the second half and the unheralded Moldovans, who had Gatcan dismissed for a second yellow late on, were unlucky not to add to their four points.
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