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}_{-0.074}^{+0.100}\,$ 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. *The HATSouth network is operated by a collaboration consisting of Princeton University (PU), the Max Planck Institute für Astronomie (MPIA), the Australian National University (ANU), and the Universidad Adolfo Ibáñez (UAI). The station at Las Campanas Observatory (LCO) of the Carnegie Institute is operated by PU in conjunction with UAI, the station at the High Energy Spectroscopic Survey (H.E.S.S.) site is operated in conjunction with MPIA, and the station at Siding Spring Observatory (SSO) is operated jointly with ANU. Based in part on observations made with the MPG 2.2 m Telescope at the ESO Observatory in La Silla. Based on observations collected at the European Southern Observatory.