Russia goalkeeper Igor Akinfeev was struck by a flare thrown from the stands almost immediately after kick-off in the Group G match, prompting a lengthy suspension in play.
The game resumed after a delay of more than half an hour, with Akinfeev taken to hospital, only for further problems to arise.
The Russian Football Union (RFU) said they would file an official protest to UEFA and the governing body has decided that Fabio Capello's side should be awarded all three points.
UEFA also ruled that Montenegro will play their next qualifier against Liechtenstein behind closed doors, with a further one game stadium ban for supporters deferred for a two-year probationary period.
The Football Association of Montenegro has also been fined €50,000 by UEFA.
Russia remain in third place, but now have eight points, with Montenegro in fourth on five points.
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