Extragalactic planetary nebulae (PNe) are not only useful as distance signposts or as tracers of the dark matter content of their host galaxies, but constitute also good indicators of the main properties of their parent stellar populations. Yet, so far, the properties of PNe in the optical regions of galaxies where stellar population gradients can be more extreme have remained largely unexplored, mainly because the detection of PNe with narrow-band imaging or slitless spectroscopy is considerably hampered by the presence of a strong stellar background. Integral field spectroscopy (IFS) can overcome this limitation, and here we present a study of the PN population in the nearby compact elliptical M32. Using SAURON data taken with just two 10-min-long pointings we have doubled the number of known PNe within the effective radius of M32, detecting PNe five times fainter than previously found in narrow-band images that collected nearly the same number of photons. We have carefully assessed the incompleteness limit of our survey, and accounting for it across the entire range of luminosity values spanned by our detected PNe, we could conclude despite having at our disposal only 15 sources that the central PNe population of M32 is consistent with the generally adopted shape for the PNe Luminosity Function and its typical normalization observed in early-type galaxies. Furthermore, owing to the proximity of M32 and to ultraviolet images taken with the Hubble Space Telescope, we could identify the most likely candidates for the central star of a subset of our detected PNe and conclude that these stars are affected by substantial amounts of circumstellar dust extinction, a finding that could reconcile the intriguing discrepancy previously reported in M32 between the model predictions and the observations for the later stages of stellar evolution. Considering the modest time investment on a 4-m-class telescope that delivered these results, this study illustrates the potential of future IFS investigations for the central PNe population of early-type galaxies, either with existing SAURON data for many more, albeit more distant, objects, or from campaigns that will use the future generations of integral field spectrographs that will be mounted on 8-m-class telescopes, such as MUSE on the Very Large Telescope.