We develop a time-domain numerical framework for global scalar wave scattering in Minkowski spacetime. The main contribution is an exact conformal matching of three compactified regions: a past hyperboloidal domain attached to $\mathscr I^-$, a Penrose domain covering a neighborhood of spatial infinity $i^0$, and a future hyperboloidal domain attached to $\mathscr I^+$. The matching surfaces are identical conformal hypersurfaces in the adjacent charts. This yields a global evolution scheme connecting $\mathscr I^-$, the neighborhood of $i^0$, and $\mathscr I^+$ without artificial timelike outer boundaries and without interpolation between scri-fixing gauges. We implement the construction for spherically symmetric scalar waves, including free propagation, localized linear scattering potentials such as the Pöschl–Teller potential, and semilinear wave equations with cubic, quintic, and septic nonlinearities. The numerical experiments demonstrate stable propagation across the matching interfaces, direct extraction of radiation at $\mathscr I^+$, and fourth-order convergence for the free and linear-potential tests. The quintic and septic nonlinear tests exhibit approximately fourth-order convergence and recover the expected late-time tail rates. The cubic case, by contrast, shows only first-order convergence, revealing a limitation of our treatment near compactified boundaries when the conformally rescaled nonlinear source remains non-vanishing. These results validate the conformal matching strategy for long-time simulations, while identifying the boundary regularity issues that must be addressed using a more robust treatment of spatial infinity.