A class of event-triggered stabilization technique works with a small-gain theorem, when the controlled system has a certain input-to-state stability (ISS) property from the measurement (sensor) disturbance to state. However, such an ISS property is not always achievable for nonlinear systems. In particular, early research suggests that global internal stabilizability does not imply global external stabilizability even for small sensor disturbances. This note proposes a new event-triggered stabilization technique that requires a milder condition that the controlled system has a certain ISS property from the input (actuator) disturbance to state. The technique is further applied to explicitly construct an event-triggered controller for the output regulation problem of a class of nonlinear systems. With the design, Zeno behavior is avoided.