Broken-gap (type-III) two-dimensional (2D) van der Waals heterostructures (vdWHs) offer an ideal platform for interband tunneling devices due to their broken-gap band offset and sharp band edge. Here, we demonstrate an efficient control of energy band alignment in a typical type-III vdWH, which is composed of vertically-stacked molybdenum telluride (MoTe2) and tin diselenide (SnSe2), via both electrostatic and optical modulation. By a single electrostatic gating with hexagonal boron nitride (h-BN) as the dielectric, a variety of electrical transport characteristics including forward rectifying, Zener tunneling, and backward rectifying are realized on the same heterojunction at low gate voltages of ±1 V. In particular, the heterostructure can function as an Esaki tunnel diode with a room-temperature negative differential resistance. This great tunability originates from the atomically-flat and inert surface of h-BN that significantly suppresses the interfacial trap scattering and strain effects. Upon the illumination of an 885 nm laser, the band alignment of heterojunction can be further tuned to facilitate the direct tunneling of photogenerated charge carriers, which leads to a high photocurrent on/off ratio of > 10 5 and a competitive photodetectivity of 1.03 × 1012 Jones at zero bias. Moreover, the open-circuit voltage of irradiated heterojunction can be switched from positive to negative at opposite gate voltages, revealing a transition from accumulation mode to depletion mode. Our findings not only promise a simple strategy to tailor the bands of type-III vdWHs but also provide an in-depth understanding of interlayer tunneling for future low-power electronic and optoelectronic applications.