We present the first direct measurement of an astrophysical reaction using a radioactive beam of isomeric nuclei. In particular, we have measured the strength of the key 447-keV resonance in the ^{26m}Al(p,γ)^{27}Si reaction to be 432_{-226}^{+146} meV and find that this resonance dominates the thermally averaged reaction rate for temperatures between 0.3 and 2.5 GK. This work represents a critical development in resolving one of the longest standing issues in nuclear astrophysics research, relating to the measurement of proton capture reactions on excited quantum levels, and offers unique insight into the destruction of isomeric ^{26}Al in astrophysical plasmas.