Interferometric phase measurement is widely used to precisely determine quantities such as length, speed and material properties1,2,3. Without quantum correlations, the best phase sensitivity \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}\) achievable using n photons is the shot-noise limit, \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}=1\,/\sqrt{{n}}\). Quantum-enhanced metrology promises better sensitivity, but, despite theoretical proposals stretching back decades3,4, no measurement using photonic (that is, definite photon number) quantum states has truly surpassed the shot-noise limit. Instead, all such demonstrations, by discounting photon loss, detector inefficiency or other imperfections, have considered only a subset of the photons used. Here, we use an ultrahigh-efficiency photon source and detectors to perform unconditional entanglement-enhanced photonic interferometry. Sampling a birefringent phase shift, we demonstrate precision beyond the shot-noise limit without artificially correcting our results for loss and imperfections. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.