We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.