The effect of differently oriented magnetic field on chiral incommensurate helimagnet UPtGe is studied both experimentally and theoretically. The magnetization measurements up to the field above the saturation have revealed an isotropic magnetic response below 20 T and a remarkable nonmonotonic anisotropy in high fields. Moreover, the two principally different phase transitions from the noncollinear incommensurate to the field-induced ferromagnetic state have been observed. These properties are successfully explained by density-functional theory calculations taking into account the noncollinearity of the magnetic structures, arbitrary directed magnetic field, and relativistic effects. We also estimate the strength of different competing magnetic interactions and discuss possible scenarios of the field-induced phase transformations.