Passive acoustic mapping (PAM) is an algorithm that reconstructs the location of acoustic sources using an array of receivers. This technique can monitor therapeutic ultrasound procedures to confirm the spatial distribution and amount of microbubble activity induced. Current PAM algorithms have an excellent lateral resolution but have a poor axial resolution, making it difficult to distinguish acoustic sources within the ultrasound beams. With recent studies demonstrating that short-length and low-pressure pulses-acoustic wavelets-have the therapeutic function, we hypothesized that the axial resolution could be improved with a quasi-pulse-echo approach and that the resolution improvement would depend on the wavelet's pulse length. This article describes an algorithm that resolves acoustic sources axially using time of flight and laterally using delay-and-sum beamforming, which we named axial temporal position PAM (ATP-PAM). The algorithm accommodates a rapid short pulse (RaSP) sequence that can safely deliver drugs across the blood-brain barrier. We developed our algorithm with simulations (k-wave) and in vitro experiments for one-, two-, and five-cycle pulses, comparing our resolution against that of two current PAM algorithms. We then tested ATP-PAM in vivo and evaluated whether the reconstructed acoustic sources mapped to drug delivery within the brain. In simulations and in vitro, ATP-PAM had an improved resolution for all pulse lengths tested. In vivo, experiments in mice indicated that ATP-PAM could be used to target and monitor drug delivery into the brain. With acoustic wavelets and time of flight, ATP-PAM can locate acoustic sources with a vastly improved spatial resolution.