Cryo-electron tomography (cryo-ET) allows cellular ultrastructures and macromolecular complexes to be imaged in three-dimensions in their native environments. Cryo-electron tomograms are reconstructed from projection images taken at defined tilt-angles. In order to recover high-resolution information from cryo-electron tomograms, it is necessary to measure and correct for the contrast transfer function (CTF) of the microscope. Most commonly, this is performed using protocols that approximate the sample as a two-dimensional (2D) plane. This approximation accounts for differences in defocus and therefore CTF across the tilted sample. It does not account for differences in defocus of objects at different heights within the sample; instead, a 3D approach is required. Currently available approaches for 3D-CTF correction are computationally expensive and have not been widely implemented. Here we simulate the benefits of 3D-CTF correction for high-resolution subtomogram averaging, and present a user-friendly, computationally-efficient 3D-CTF correction tool, NovaCTF, that is compatible with standard tomogram reconstruction workflows in IMOD. We validate the approach on synthetic data and test it using subtomogram averaging of real data. Consistent with our simulations, we find that 3D-CTF correction allows high-resolution structures to be obtained with much smaller subtomogram averaging datasets than are required using 2D-CTF. We also show that using equivalent dataset sizes, 3D-CTF correction can be used to obtain higher-resolution structures. We present a 3.4 angstrom resolution structure determined by subtomogram averaging.