Dinamo Moscow striker Kerzakhov, recalled after an absence of almost 19 months, opened the scoring from Andrei Arshavin's 27th-minute pass before converting a rebound early in the second half, with Konstantin Zyryanov capping an impressive victory in the 71st minute.
Guus Hiddink's side host Germany in October in a game that could decide which team qualifies automatically for next summer's showpiece in South Africa and which team must make do with a place in the play-offs alongside the seven other best runners-up.
Germany's next game sees them travel to Azerbaijan in August before Russia host Liechtenstein early in September. Sweden kept their slim qualification hopes intact with an emphatic 4-0 victory at home to Group One's bottom side Malta, with goals from Kim Kallstrom, Daniel Majstorovic, star striker Zlatan Ibrahimovic and Marcus Berg.
Lars Lagerback's men are now level on nine points with third-placed Portugal, seven points behind group leaders Denmark but only four points off second-placed Hungary and a possible play-off spot. In Group Six, Ukraine moved level on points with second-placed Croatia after coming from behind to secure a narrow 2-1 win at home to Kazakhstan.
Tanat Nuserbayev gave the visitors, who are ranked 132nd in the world, a surprise 19th-minute lead, only for Sergiy Nazarenko to score either side of half-time to rescue victory for Ukraine, who reached the last eight at the 2006 world finals. Earlier, Aco Stojkov's 10th-minute header and a late strike from Filip Ivanovski allowed Macedonia to overcome Iceland 2-0 in Skopje and move level with second-placed Scotland in group nine.