We report the discovery of two new transiting extrasolar planets. HAT-P-18b orbits the V=12.759 K2 dwarf star GSC 2594-00646, with a period P=5.508023+/-0.000006 days, transit epoch T_c_=2454715.02174+/-0.00020(BJD), and transit duration 0.1131+/-0.0009 days. The host star has a mass of 0.77+/-0.03M_{sun}, radius of 0.75+/-0.04R{sun}, effective temperature 4803+/-80K, and metallicity [Fe/H]=+0.10+/-0.08. The planetary companion has a mass of 0.197+/-0.013M_J and radius of 0.995+/-0.052R_J_, yielding a mean density of 0.25+/-0.04g/cm^3^. HAT-P-19b orbits the V=12.901 K1 dwarf star GSC 2283-00589, with a period P=4.008778+/-0.000006 days, transit epoch T_c_=2455091.53417+/-0.00034(BJD), and transit duration 0.1182+/-0.0014 days. The host star has a mass of 0.84+/-0.04M_{sun}, radius of 0.82+/-0.05R{sun}, effective temperature 4990+/-130K, and metallicity [Fe/H]=+0.23+/-0.08. The planetary companion has a mass of 0.292+/-0.018M_J and radius of 1.132+/-0.072R_J_, yielding a mean density of 0.25+/-0.04g/cm^3^. The radial velocity residuals for HAT-P-19 exhibit a linear trend in time, which indicates the presence of a third body in the system. Comparing these observations with theoretical models, we find that HAT-P-18b and HAT-P-19b are each consistent with a hydrogen-helium-dominated gas giant planet with negligible core mass. HAT-P-18b and HAT-P-19b join HAT-P-12b and WASP-21b in an emerging group of low-density Saturn-mass planets, with negligible inferred core masses. However, unlike HAT-P-12b and WASP-21b, both HAT-P-18b and HAT-P-19b orbit stars with super-solar metallicity.