Squeezing-assisted interferometers achieve sub-shot-noise sensitivity to phase shifts, but losses can strongly degrade their performance. Here we present the first experimental demonstration of detection-loss tolerance for this class of interferometers employing degenerate optical parametric amplification at one output port. For
50% detection efficiency, the phase sensitivity of any interferometer with coherent and squeezed vacuum inputs would not overcome the shot-noise limit, but in our case the output amplification gives
6 dB sub-shot-noise sensitivity. We further demonstrate that robustness increases with higher gain of the output amplifier: sub-shot-noise sensitivity is achieved for detection efficiency as low as
13%. We believe that overcoming detection inefficiency will become crucial to take full advantage of quantum metrology, for example in gravitational-wave detection, quantum sensing and imaging.