This paper investigated the quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via the event-triggered impulsive control (ETIC) approach, which integrates impulsive control and event-triggered control. The instances of impulsive activation were determined by an event-triggered mechanism based on a particular condition that depends on the system states. By employing the comparison principle for impulsive systems and the formula for variable parameters, we established the exact synchronization error bound and derived sufficient conditions for achieving quasi-synchronization. Furthermore, we proved the absence of Zeno behavior in the controlled system under the ETIC mechanism. Finally, we gave an example to verify that the theoretical results are valid under the proposed ETIC strategy.