Using a method to discover and classify supernovae (SNe) in galaxy spectra, we find 90 Type Ia SNe (SNe Ia) and 10 Type II SNe among the ~700,000 galaxy spectra in the Sloan Digital Sky Survey Data Release 7 that have VESPA-derived star-formation histories (SFHs). We use the SN Ia sample to measure SN Ia rates per unit stellar mass. We confirm, at the median redshift of the sample, z = 0.1, the inverse dependence on galaxy mass of the SN Ia rate per unit mass, previously reported by Li et al. (2011b) for a local sample. We further confirm, following Kistler et al. (2011), that this relation can be explained by the combination of galaxy "downsizing" and a power-law delay-time distribution (DTD; the distribution of times that elapse between a hypothetical burst of star formation and the subsequent SN Ia explosions) with an index of -1, inherent to the double-degenerate progenitor scenario. We use the method of Maoz et al. (2011) to recover the DTD by comparing the number of SNe Ia hosted by each galaxy in our sample with the VESPA-derived SFH of the stellar population within the spectral aperture. In this galaxy sample, which is dominated by old and massive galaxies, we recover a "delayed" component to the DTD of 4.5 +/- 0.6 (statistical) +0.3 -0.5 (systematic) X 10^-14 SNe Msun^-1 yr^-1 for delays in the range > 2.4 Gyr. The mass-normalized SN Ia rate, averaged over all masses and redshifts in our galaxy sample, is R(Ia,M,z=0.1) = 0.10 +/- 0.01 (statistical) +/- 0.01 (systematic) SNuM, and the volumetric rate is R(Ia,V,z=0.1) = 0.247 +0.029 -0.026 (statistical) +0.016 -0.031 (systematic) X 10^-4 SNe yr^-1 Mpc^-3. This rate is consistent with the rates and rate evolution from other recent SN Ia surveys, which together also indicate a ~t^-1 DTD.