We show that modulating the diode-pump power of a microchip solid-state laser enables to lock its wavelength to a reference molecular line. The method is applied to two different types of Er,Yb:glass monolithic microchip lasers operating at 1.53 microm. First, wavelength locking of a continuous-wave dual-polarization microchip laser to acetylene absorption lines is demonstrated, without using any additional modulator, internal or external. We then show that, remarkably, this simple method is also suitable for stabilizing a passively Q-switched microchip laser. A pulsed wavelength stability of 10(-8) over 1 hour is readily observed. Applications to lidars and to microwave photonics are discussed.