The home side then threw caution to wind and pushed forward in search of an equalizer, which they scored ten minutes from the end through Hoewedes, whose header after a corner gave goalkeeper Andre Lenz no chance.
But even before the stadium announcer had finished announcing the name of the scorer, Dzeko restored the visitors' lead after being set up Makoto Hasebe.
Former Germany striker Kevin Kuranyi thought he had levelled matters again when his header crashed against the upright and then seemed to cross the line, but the referee again waved play on.
The win sees Armin Veh's side move to five in the table on nine points, while Schalke remain third on ten.
Table-topping SV Hamburg and second-placed Bayer Leverkusen are on 13 points ahead of their games on the weekend.