Only a few years ago, it was realized that the zero-area Sagnac interferometer topology is able to perform quantum nondemolition measurements of position changes of a mechanical oscillator. Here, we experimentally show that such an interferometer can also be efficiently enhanced by squeezed light. We achieved a nonclassical sensitivity improvement of up to 8.2 dB, limited by optical loss inside our interferometer. Measurements performed directly on our squeezed-light laser output revealed squeezing of 12.7 dB. We show that the sensitivity of a squeezed-light enhanced Sagnac interferometer can surpass the standard quantum limit for a broad spectrum of signal frequencies without the need for filter cavities as required for Michelson interferometers. The Sagnac topology is therefore a powerful option for future gravitational-wave detectors, such as the Einstein Telescope, whose design is currently being studied.