The match was all but over as a contest inside 20 minutes as Kerzhakov and Alexander Kokorin put the visitors 2-0 up in Ramat Gan. Kerzhakov made it 3-0 in the 64th minute and Victor Fayzulin added a fourth as Fabio Capello's side made it two wins from two qualifiers.
The opening goal came from a free-kick in the sixth minute. Having been fouled by Tal Ben Haim, Kerzhakov stepped up to fire the ball into the top left corner from around 25 yards.
He dragged another effort wide and the opening exchanges were generally scrappy, but Russia doubled their advantage in the 18th minute when Kokorin beat Mallorca goalkeeper Dudu Aouate from 12 yards.
The visitors were dominant and could have had more goals before the interval, but Denis Glushakov's and Vasili Berezutskiy's efforts were too high and Aouate saved unconvincingly from Kerzhakov.
But Israel enjoyed a spell of pressure shortly before the interval, starting when Bebras Natcho volleyed over from long range. Mahran Radi wasted a good chance to pull a goal back when his close-range volley also cleared the crossbar, and he was off target twice more in stoppage time.
Israel introduced Eden Ben Basat and Ben Sahar at the break and the former headed Natcho's free-kick over shortly afterwards.
Glushakov and Alexander Samedov threatened for Russia before Ben Basat headed Hen Ezra's corner wide. But Russia put the game well and truly to bed when Fayzulin crossed from the left and Kerzhakov slotted home from six yards.
And Fayzulin grabbed a goal of his own in the 77th minute, converting Samedov's low cross at the near post. Radi and Yoav Ziv were unable to conjure an Israeli goal as their side finished well beaten.