The relative rarity of giant planets around low-mass stars compared with solar-type stars is a key prediction from the core-accretion planet formation theory. In this paper we report on the discovery of four gas giant planets that transit low-mass late K and early M dwarfs. The planets HATS-74Ab (TOI 737b), HATS-75b (TOI 552b), HATS-76b (TOI 555b), and HATS-77b (TOI 730b) were all discovered from the HATSouth photometric survey and follow-up using TESS and other photometric facilities. We use the new ESPRESSO facility at the VLT to confirm systems and measure their masses. We find that these planets have masses of 1.46 ± 0.14 MJ, 0.491 ± 0.039 MJ, 2.629 ± 0.089 MJ, and 1.374 0.0740.100-+ MJ, respectively, and radii of 1.032 ± 0.021 RJ, 0.884 ± 0.013 RJ, 1.079 ± 0.031 RJ, and 1.165 ± 0.021 RJ, respectively. The planets all orbit close to their host stars with orbital periods ranging from 1.7319 days to 3.0876 days. With further work, we aim to test core-accretion theory by using these and further discoveries to quantify the occurrence rate of giant planets around low-mass host stars.