The Al23(p,γ)Si24 reaction is among the most important reactions driving the energy generation in type-I x-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. Here, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The Al23(d,n) reaction was used to populate the astrophysically important states in Si24. This enables a measurement in complete kinematics for extracting all relevant inputs necessary to calculate the reaction rate. For the first time, a predicted close-lying doublet of a 22+ and (41+,02+) state in Si24 was disentangled, finally resolving conflicting results from two previous measurements. Moreover, it was possible to extract spectroscopic factors using GRETINA and LENDA simultaneously. This new technique may be used to constrain other important reaction rates for various astrophysical scenarios.