We report the discovery using Spitzer's high-resolution spectrograph of seven active galactic nuclei (AGNs) in a sample of 32 late-type galaxies that show no definitive signatures of AGNs in their optical spectra. These observations suggest that the AGN detection rate in late-type galaxies is possibly 4 times larger than what optical spectroscopic observations alone suggest. We demonstrate using photoionization models with an input AGN and an extreme UV-bright starburst ionizing radiation field that the observed mid-infrared line spectrum, which includes the high-ionization [Ne V] 14 μm and/or 24 μm lines, cannot be replicated unless an AGN contribution, in some cases as little as 10% of the total galaxy luminosity, is included. These models show that when the fraction of the total luminosity due to the AGN is low, optical diagnostics are insensitive to the presence of the AGN. In this regime of parameter space, the mid-infrared diagnostics offer a powerful tool for uncovering AGNs missed by optical spectroscopy. The AGN bolometric luminosities in our sample range from ~3 × 10⁴¹ to ~2 × 10⁴³ ergs s⁻¹, which, based on the Eddington limit, corresponds to a lower mass limit for the black hole that ranges from ~3 × 10³ to as high as ~1.5 × 10⁵ M. These lower mass limits, however, do not put a strain on the well-known relationship between the black hole mass and the host galaxy's stellar velocity dispersion established in predominantly early-type galaxies. Our findings add to the growing evidence that black holes do form and grow in low-bulge environments and that they are significantly more common than optical studies indicate.