This Rapid Communication reports on the discovery of a route to bursting, called a pulse-shaped explosion (PSE), for a paradigmatic class of nonlinear oscillators. We find that both an equilibrium and a limit cycle can exhibit pulse-shaped sharp quantitative changes in relation to the variation of system parameters, which are interesting explosive behaviors, the PSE. It leads to large-amplitude oscillations in the rest phase (i.e., small-amplitude oscillations) of bursting, giving rise to additional active phases alternating with the rest phase, and finally determines compound bursting structures. This way, the route to complex bursting dynamics by PSE is explained and its robustness is shown. PSE opens different ways for the control dynamics of complex systems.