The astrophysical 25Al(p,γ)26Si reaction represents one of the key remaining uncertainties in accurately modeling the abundance of radiogenic 26Al ejected from classical novae. Specifically, the strengths of key proton-unbound resonances in 26Si, that govern the rate of the 25Al(p,γ) reaction under explosive astrophysical conditions, remain unsettled. Here, we present a detailed spectroscopy study of the 26Si mirror nucleus 26Mg. We have measured the lifetime of the 3+, 6.125-MeV state in 26Mg to be 19(3)fs and provide compelling evidence for the existence of a 1− state in the T=1,A=26 system, indicating a previously unaccounted for ℓ=1 resonance in the 25Al(p,γ) reaction. Using the presently measured lifetime, together with the assumption that the likely 1− state corresponds to a resonance in the 25Al+p system at 435.7(53) keV, we find considerable differences in the 25Al(p,γ) reaction rate compared to previous works. Based on current nova models, we estimate that classical novae may be responsible for up to ≈15% of the observed galactic abundance of 26Al.