The heavy-ion, fusion-evaporation reaction C-12(O-16,n) was used to identify gamma-decay transitions from excited states in Si-27 above the proton threshold. The precise level energy measurements, J(pi) assignments, and lifetime measurements of astrophysically important Al-26(m)+p resonances have allowed an evaluation of the Al-26(m)(p,gamma)Si-27 reaction rate. An l(p)=0 resonance has been newly identified at a center-of-mass energy in the Al-26(m)+p system of 146.3(3) keV and is expected to dominate the rate for low stellar temperatures. In addition, an l(p)=1 resonance has been identified at 378.3(30) keV and is likely to dominate the rate at high astrophysical temperatures, such as those found in oxygen-neon novae and core-collapse supernovae.