Winger Rieko Ioane grabbed his seventh try of the season to secure the Blues their third win in succession as the home side held on after being reduced to 14 men late at Eden Park.
Blues winger Tanielu Tele'a scored a first-half try but was handed a red card in the 70th minute after a dangerous aerial clash that flattened his opposite number Dillyn Leyds.
Stormers replacement back SP Marais then missed the simplest of penalty goals that would have trimmed the lead to five points, allowing Ioane to put the game beyond the South African swith a clever step and try at the left corner with five minutes left.
Flyhalf Otere Black grabbed the Blues' second try under the posts in the 62nd minute after a brilliant off-load by Sonny Bill Williams, while the Stormers, who suffered their third loss, were held try-less.