Didier Drogba, making his first appearance in the Champions League this season after suspension and injury, added the second with a 62nd-minute penalty before Ivanovic scored with a header and a right-foot drive.
Chelsea now have four wins in four games in the group.
Nikita Bazhenov replied for Spartak, who are third in the table with six points, in the 86th minute.
It was all very comfortable in the end for Chelsea, with Drogba captaining the side in the absence of the rested John Terry.
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