Magnetoelectric coupling(1,2) between magnetic and electrical properties presents valuable degrees of freedom for applications. The two most promising scenarios are magnetic-field sensors(3) that could replace low-temperature superconducting quantum interference devices, and electric-write magnetic-read memory devices that combine the best(2) of ferroelectric and magnetic random-access memory. The former scenario requires magnetically induced continuous and reversible changes in electrical polarization. These are commonly observed, but the coupling constants thus obtained are invalid for data-storage applications, where the more difficult to achieve(4,5) and rarely studied magnetic response to an electric field is required. Here, we demonstrate electrically induced giant, sharp and persistent magnetic changes (up to 2.3 x 10(-7) sm(-1)) at a single epitaxial interface in ferromagnetic 40 nm La0.67Sr0.33MnO3 films on 0.5 mm ferroelectric BaTiO3 substrates. X-ray diffraction confirms strain coupling via ferroelastic non-180 degrees BaTiO3 domains. Our findings are valid over a wide range of temperatures including room temperature, and should inspire further study with single epitaxial interfaces.