The origin and source rocks of alkali-rich and SiO2-undersatured magmas in the Earth’s upper mantle are still under debate. The garnet signature in rare earth element patterns of such magmas suggests a garnet-bearing source rock, which could be garnet lherzolite or garnet pyroxenite. Partial melting experiments were performed at 2.8 GPa and 1345–1445 °C in a piston-cylinder using mixtures of natural lherzolite with either 0.4 wt% H2O and 0.4 wt% CO2 or 0.7 wt% H2O and 0.7 wt% CO2. Different designs of AuPd capsules were used for melt extraction. The most successful design included a pentagonally shaped disc placed in the top part of the capsule for sufficient melt extraction. The degrees of partial melting range from 0.2 to 0.04 and decrease with decreasing temperature and volatile content. All samples contain olivine and orthopyroxene. The amounts of garnet and clinopyroxene decrease with increasing degree of partial melting until both minerals disappear from the residue. Depending on the capsule design, the melts quenched to a mixture of quench crystals and residual glass or to glass, allowing measurement of the volatile concentrations by Raman spectroscopy. The compositions of the partial melts range from basalts through picrobasalts to foidites. Compared to literature data for melting of dry lherzolites, the presence of H2O and CO2 reduces the SiO2 concentration and increases the MgO concentration of partial melts, but it has no observable effect on the enrichment of Na2O in the partial melts. The partial melts have compositions similar to natural melilitites from intraplate settings, which shows that SiO2-undersaturated intraplate magmas can be generated by melting of garnet lherzolite in the Earth’s upper mantle in the presence of H2O and CO2.