Detecting acoustic transients by signal-to-noise ratio (SNR) becomes problematic in nonstationary ambient noise environments characteristic of coral reefs. An alternate approach presented here uses signal directionality to automatically detect and localize transient impulsive sounds collected on underwater vector sensors spaced tens of meters apart. The procedure, which does not require precise time synchronization, first constructs time-frequency representations of both the squared acoustic pressure (spectrogram) and dominant directionality of the active intensity (azigram) on each sensor. Within each azigram, sets of time-frequency cells associated with transient energy arriving from a consistent azimuthal sector are identified. Binary image processing techniques then link sets that share similar duration and bandwidth between different sensors, after which the algorithm triangulates the source location. Unlike most passive acoustic detectors, the threshold criterion for this algorithm is bandwidth instead of pressure magnitude. Data collected from shallow coral reef environments demonstrate the algorithm's ability to detect SCUBA bubble plumes and consistent spatial distributions of somniferous fish activity. Analytical estimates and direct evaluations both yield false transient localization rates from 3% to 6% in a coral reef environment. The SNR distribution of localized pulses off Hawaii has a median of 7.7 dB and interquartile range of 7.1 dB.