The nature of dark matter is a longstanding mystery in cosmology, which can be studied with laboratory or collider experiments, as well as astrophysical and cosmological observations. In this work, we propose realistic and efficient strategies to detect radiative products from dark-matter decays with line-intensity mapping (LIM) experiments. This radiation will behave as a line interloper for the atomic and molecular spectral lines targeted by LIM surveys. The most distinctive signatures of the contribution from dark-matter radiative decays are an extra anisotropy on the LIM power spectrum due to projection effects, as well as a narrowing and a shift towards higher intensities of the voxel intensity distribution. We forecast the minimum rate of decays into two photons that LIM surveys will be sensitive to as function of the dark-matter mass in the range $sim 10^{-6}-10$ eV, and discuss how to reinterpret such results for dark matter that decays into a photon and another particle. We find that both the power spectrum and the voxel intensity distribution are expected to be very sensitive to the dark-matter contribution, with the voxel intensity distribution being more promising for most experiments considered. Interpreting our results in terms of the axion, we show that LIM surveys will be extremely competitive to detect its decay products, improving several orders of magnitudes (depending on the mass) the sensitivity of laboratory and astrophysical searches, especially in the mass range $sim 1-10$ eV.