Strikes from Vasili Berezutski, Alexander Kokorin and Denis Glushakov gave the hosts a 3-1 win and restored their single-point lead at the top of the group over key rivals Portugal.
Capello's men now need to take maximum points from their last two games away to group minnows Luxembourg and Azerbaijan next month in order to seal automatic qualification.
The hosts had looked nervous in a tight first period in which solid Israeli defending looked to keep alive their own slim hopes of muscling in on a top two place.
Zenit St Petersburg striker Roman Shirokov came close twice in the early stages on his home ground, but there was frustration among his team-mates as the first half ended goalless.
Russian pressure finally eased five minutes into the second half when lanky defender Berezutski rose highest to head home a Shirokov cross and net the opener.
And Russia had doubled their lead within two minutes after Kokorin steered a right-foot shot into the top corner after being set up by Alexander Samedov.
Russia secured victory in the 74th minute with a third goal but only after Israeli keeper Dudu Aouate had denied Shirokov from the spot.
Awarded a penalty after Eran Zehavi handled Alan Dzagoev's flick in the box, Shirokov saw his shot superbly tipped onto the post by Aouate - only for Glushakov to react fastest and steer the rebound home.
Israel grabbed a consolation for the visitors in injury time when a cross from Ofir Davidadze struck the shoulder of Eran Zehavi and deflected past Russian keeper Igor Akinfeev.