Zetterberg also notched two assists, and Pavel Datsyuk had a goal and a pair of assists for the Wings, who have won three in a row.
Ferriero cut Detroit's lead to 3-2 with a goal at 4:52 of the second period. Eaves' tip-in at 19:49 of the period proved to be the decisive goal.
San Jose has flattened out to a 2-3-2 record over their last seven contests and has settled into the cellar of the Pacific Division. Detroit leads the Central Division by four points over the defending Stanley Cup champion Chicago Black Hawks.
Ohio crash that killed two caught on camera [VIDEO]
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees