We use the Wide-field Infrared Survey Explorer (WISE) and the Sloan Digital Sky Survey (SDSS) to confirm a connection between dust-obscured active galactic nuclei (AGNs) and galaxy merging. Using a new, volume-limited (z<=0.08) catalogue of visually selected major mergers and galaxy-galaxy interactions from the SDSS, with stellar masses above 2x10^10^M_{sun}_, we find that major mergers (interactions) are 5-17 (3-5) times more likely to have red [3.4]-[4.6] colours associated with dust-obscured or 'dusty' AGNs, compared to non-merging galaxies with similar masses. Using published fibre spectral diagnostics, we map the [3.4]-[4.6] versus [4.6]-[12] colours of different emission-line galaxies and find that one-quarter of Seyferts have colours indicative of a dusty AGN. We find that AGNs are five times more likely to be obscured when hosted by a merging galaxy, half of AGNs hosted by a merger are dusty, and we find no enhanced frequency of optical AGNs in merging over non-merging galaxies. We conclude that undetected AGNs missed at shorter wavelengths are at the heart of the ongoing AGN-merger connection debate. The vast majority of mergers hosting dusty AGNs are star forming and located at the centres of M_halo_<10^13^Mc1l_{sun}_ groups. Assuming plausibly short-duration dusty-AGN phases, we speculate that a large fraction of gas-rich mergers experience a brief obscured AGN phase, in agreement with the strong connection between central star formation and black hole growth seen in merger simulations.