Tottenham Hotspur striker Roman Pavlyuchenko and Zenit midfielder Konstantin Zyryanov scored a goal apiece in the hosts' first game against their former compatriots.
The result left Russia second in the pool on nine points from four matches, one point behind the leaders Germany, who play Liechtenstein later today.
Russia seized the initiative right from kick-off, and quickly began testing the visitors' defence for weaknesses.
However, a lack of shooting accuracy, combined with some stout Azeri defending, meant the opening half-hour was goalless.
In the 32nd minute, the visitors' resistance finally crumbled when Pavlyuchenko beat goalkeeper Farkhad Veliyev with a 25-yard free-kick.
Russia created several more scoring chances but failed to increase their lead before the half-time break.
Russia continued to dominate possession in the second period, and in the 71st minute they doubled their advantage, with Zyryanov firing in from the edge of the six-yard box, after a razor-sharp pass from Pavlyuchenko, to secure a well-deserved win.