Methods that combine targeted techniques and chemometrics for analyzing food authenticity can only facilitate the detection of predefined or known adulterants, while unknown adulterants cannot be detected using such methods. Therefore, the non-targeted detection of adulterants in food products is currently in great demand. In this study, FT-IR and FT-NIR spectroscopic techniques were used in combination with non-targeted chemometric approaches, such as one-class partial least squares (OCPLS) and data-driven soft independent modeling of class analogy (DD-SIMCA), to detect adulterants in almond powder adulterated with apricot and peanut powders. The reflectance spectra of 100 pure almond powder samples from two different varieties (50 each) were collected to develop a calibration model based on each spectroscopic technique; each model was then evaluated for four independent sets of two varieties of almond powder samples adulterated with different concentrations of apricot and peanut powders. Classification using both techniques was highly sensitive, the OCPLS approach yielded 90–100% accuracy in different varieties of samples with both spectroscopic techniques, and the DD-SIMCA approach achieved the highest accuracy of 100% when used in combination with FT-IR in all validation sets. Moreover, DD-SIMCA, combined with FT-NIR, achieved a detection accuracy between 91% and 100% for the different validation sets and the misclassified samples belong to the 5% and 7% adulteration sets. These results suggest that spectroscopic techniques, combined with one-class classifiers, can be used effectively in the high-throughput screening of potential adulterants in almond powder.