The French striker scored the Baggies' second goal and his seventh in seven games since joining the club on a free transfer in July.
Markus Rosenburg gave the home side the lead, side-footing home Anelka's cross in the 32nd minute.
And it was 2-0 soon after as Anelka reacted quickest in the box to collect James Morrison's pass and skip round the keeper before finishing.
Albion's other summer recruit, Diego Lugano, was named on the bench but came on the final half hour.
He had little to do against a shot-shy Serie A side, who forced only one save from Ben Foster when Francesco Della Rocca's fierce 15-yard volley drew a smart parry from the England keeper.