We present combined experimental and theoretical investigations of the picosecond emission dynamics of broad-area semiconductor lasers (BALs). We enhance the weak longitudinal self-mode-locking that is inherent to BALs by injecting a single optical 50-ps pulse, which triggers the output of a distinct regular train of 13-ps pulses. Modeling based on multimode Maxwell-Bloch equations illustrates how the dynamic interaction of the injected pulse with the internal laser field efficiently couples the longitudinal modes and synchronizes the output across the laser stripe. Thus, our results reveal insight into the complex interplay between lateral and longitudinal dynamics in BALs, at the same time indicating their potential for short optical pulse generation.