Schieber's 57th-minute strike was enough to secure three points for the German giant, which progresses to the knockout stages of the competition unbeaten.
Dortmund's victory resigns the Sky Blues to a season without European football, as the English champions bow out with a new record for the lowest Champions League points tally achieved by an English side.
"I'm very happy that I managed to score my first Champions League goal," the Dortmund man told reporters. "Our squad consists of 21 players and we can all contribute to the success.
"We are very satisfied with this victory."