The performance of electronic and optoelectronic devices based on two-dimensional (2D) materials could be significantly affected by the electrical contacts. In search of low-resistance contacts with transition-metal dichalcogenides (TMDs), we combine density functional calculations with quantum transport simulations to investigate the structural and electronic properties of the van der Waals (vdW) heterostructures MSe2/NbSe2 (M = Mo and W). The formation of a p-type Schottky contact at the MSe2/NbSe2 interface with small Schottky barriers (0.37 eV for MoSe2/NbSe2 and 0.18 eV for WSe2/NbSe2) is demonstrated. The low Schottky barrier heights indicate a low contact resistance, which is beneficial for electron injection and low-resistance. Remarkably, we demonstrate that the Schottky barrier can be effectively tuned via the application of vertical compressive pressure, an external electrical field and tensile strain. Finally, the results are supported by quantum transport simulation, which further proves the highly transparent contacts and promising application potential in field-effect transistors (FET). Therefore, our formalism and findings not only provide insights into the MSe2/NbSe2 interfaces but also help in the design of MSe2 monolayer-based devices.