Future space telescopes with coronagraph instruments will use a wavefront sensor (WFS) to measure and correct for phase errors and stabilize the stellar intensity in high-contrast images. The HabEx and LUVOIR mission concepts baseline a Zernike wavefront sensor (ZWFS), which uses Zernike’s phase contrast method to convert phase in the pupil into intensity at the WFS detector. In preparation for these potential future missions, we experimentally demonstrate a ZWFS in a coronagraph instrument on the Decadal Survey Testbed in the High Contrast Imaging Testbed facility at NASA’s Jet Propulsion Laboratory. We validate that the ZWFS can measure low- and mid-spatial frequency aberrations up to the control limit of the deformable mirror (DM), with surface height sensitivity as small as 1 pm, using a configuration similar to the HabEx and LUVOIR concepts. Furthermore, we demonstrate closed-loop control, resolving an individual DM actuator, with residuals consistent with theoretical models. In addition, we predict the expected performance of a ZWFS on future space telescopes using natural starlight from a variety of spectral types. The most challenging scenarios require ∼1 h of integration time to achieve picometer sensitivity. This timescale may be drastically reduced by using internal or external laser sources for sensing purposes. The experimental results and theoretical predictions presented here advance the WFS technology in the context of the next generation of space telescopes with coronagraph instruments.