We investigate quasi-periodic (QP) vibration-based energy harvesting (EH) in a harmonically excited van der Pol oscillator coupled to a delayed piezoelectric coupling mechanism. The case of primary resonance, for which the frequency of the harmonic excitation is near the natural frequency of the oscillator, is considered. Analytical approximation of the QP response and the corresponding power output are obtained using the double-step multiple scales method. The effect of the time delay on the EH performance is studied. It is shown that for appropriate combination of time delay parameters, QP vibration can be used to scavenge energy over a broadband of the excitation frequency away from the resonance with a better performance.