Novel technologies in seismic data acquisition allow for recording full vector-acoustic (VA) data: pointwise recordings of pressure and its multicomponent gradient, excited by pressure only as well as dipole/gradient sources. Building on recent connections between imaging and seismic interferometry, we present a wave-equation-based, nonlinear, reverse-time imaging approach that takes full advantage of dual-source multicomponent data. The method's formulation relies on source-receiver scattering reciprocity, thus making proper use of VA fields in the wavefield extrapolation and imaging condition steps in a self-consistent manner. The VA imaging method is capable of simultaneously focusing energy from all in-and outgoing waves: The receiver-side up-and downgoing (receiver ghosts) fields are handled by the VA receiver extrapolation, whereas source-side in-and outgoing (source ghosts) arrivals are accounted for when combining dual-source data at the imaging condition. Additionally, VA imaging handles image amplitudes better than conventional reverse-time migration because it properly handles finite-aperture directivity directly from dual-source, 4C data. For nonlinear imaging, we provide a complete source-receiver framework that relies only on surface integrals, thus being computationally applicable to practical problems. The nonlinear image can be implicitly interpreted as a superposition of several nonlinear interactions between scattering components of data with those corresponding to the extrapolators (i.e., to the model). We demonstrate various features of the method using synthetic examples with complex subsurface features. The numerical results show, e.g., that the dual-source, VA image retrieves subsurface features with "super-resolution", i.e., with resolution higher than the limits of Born imaging, but at the cost of introducing image artifacts not present in the linear image. Although the method does not require any deghosting as a preprocessing step, it can use separated up-and downgoing fields to generate independent subsurface images.