Narrow linewidth is a long-pursued goal in precision measurement and sensing. We propose a parity-time symmetric (PT-symmetric) feedback method to narrow the linewidths of resonance systems. By using a quadrature measurement-feedback loop, we transform a dissipative resonance system into a PT-symmetric system. Unlike the conventional PT-symmetric systems that typically require two or more modes, here the PT-symmetric feedback system contains only a single resonance mode, which greatly extends the scope of applications. The method enables remarkable linewidth narrowing and enhancement of measurement sensitivity. We illustrate the concept in a thermal ensemble of atoms, achieving a 48-fold narrowing of the magnetic resonance linewidth. By applying the method in magnetometry, we realize a 22-times improvement of the measurement sensitivity. This work opens the avenue for studying non-Hermitian physics and high-precision measurements in resonance systems with feedback.