Russia dominated possession but found it hard to create chances until they went in front in the 38th minute.
Following a good exchange down the right between Igor Smolnikov and Roman Shirokov, Zenit St Petersburg forward Artem Dzyuba was left with the easiest of tasks to slot the only goal past keeper Andreas Isaksson.
Russia now have 11 points from seven matches in Group G, one behind second-placed Sweden. Austria lead the way with 19 points after defeating rock bottom Moldova 1-0 on Saturday.
Visiting coach Erik Hamren sprang a surprise at the start of the second half by taking off talisman Zlatan Ibrahimovic who was largely devoid of service during the first period.
Ibrahimovic's replacement Ola Toivonen was certainly more lively than his illustrious team mate and helped create Sweden's best chance of the game but Emil Forsberg could only hit his shot into the side-netting.
Sweden pressed in search of an equaliser but another Forsberg effort was excellently cut out by the impressive Smolnikov as a tiring Russia managed to hold on for the three points.
(Editing by Tony Jimenez)
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