Tottenham Hotspur striker Roman Pavlyuchenko was the hero of the match, producing a classic hat-trick after midfielder Marcos Pizzelli put Armenia into the lead.
The win lifted Russia top of Group B with 13 points from six matches. Later today, Slovakia take on Andorra, while Republic of Ireland face FYR Macedonia in the other Group B matches.
Russia started in a lively style, but failed to create any serious threat in the opening 20 minutes.
Russia replied positively and pulled level a minute later through Pavlyuchenko, who fired the ball home from Alexander Anyukov's right-hand cross.
After the interval the hosts added power and precision to their attack and clinched the lead in the 59th minute, when Pavlyuchenko netted his second, firing in from the edge of the six-yard box.
Armenia had a clear chance to level again in the 65th minute but their forward Yura Movsisyan failed to redirect his teammate's cross into the net with a free header.
In the 73rd minute Pavlyuchenko completed his hat-trick, beating Armenia's veteran goalkeeper Roman Berezovsky with a precise spot-kick to secure Russia's well-deserved win, after the guests' captain Sargis Hovsepyan fouled Chelsea winger Yury Zhirkov in the area.
In the 85th minute Armenia forward Henrik Mkhitaryan, who plays for Ukraine's newly-crowned champions Shakhtar Donetsk, sent the ball into the net but his goal was ruled offside by French referee Stephane Lannoy.