كتب : وكالات
Terry opened the scoring when he made the most of a low corner kick by releasing a scorching shot that hit the target after going between defender Benoit Cheyrou and the post.
Anelka converted a penalty kick three minutes from the half-hour mark to ensure the hosts' superiority.
Chelsea, who had beaten Zilina 4-1 in their previous Champions League game, are now on top of Group F on goal difference with six points.
Spartak Moscow have also amassed six points from their first couple of matches. They beat Zilina 3-0 and now lie in second place.