Stars are giant thermonuclear plasma furnaces that slowly fuse the lighter elements in the universe into heavier elements, releasing energy, and generating the pressure required to prevent collapse. To understand stars, we must rely on nuclear reaction rate data obtained, up to now, under conditions very different from those of stellar cores. Here we show thermonuclear measurements of the 2 H(d, n)3 He and 3 H(t,2n)4 He S-factors at a range of densities (1.2-16 g cm-3 ) and temperatures (2.1-5.4 keV) that allow us to test the conditions of the hydrogen-burning phase of main-sequence stars. The relevant conditions are created using inertial-confinement fusion implosions at the National Ignition Facility. Our data agree within uncertainty with previous accelerator-based measurements and establish this approach for future experiments to measure other reactions and to test plasma-nuclear effects present in stellar interiors, such as plasma electron screening, directly in the environments where they occur.