Correlation constrained multivariate curve resolution-alternating least-squares is shown to be a feasible method for processing first-order instrumental data and achieve analyte quantitation in the presence of unexpected interferences. Both for simulated and experimental data sets, the proposed method could correctly retrieve the analyte and interference spectral profiles and perform accurate estimations of analyte concentrations in test samples. Since no information concerning the interferences was present in calibration samples, the proposed multivariate calibration approach including the correlation constraint facilitates the achievement of the so-called second-order advantage for the analyte of interest, which is known to be present for more complex higher-order richer instrumental data. The proposed method is tested using a simulated data set and two experimental data systems, one for the determination of ascorbic acid in powder juices using UV-visible absorption spectral data, and another for the determination of tetracycline in serum samples using fluorescence emission spectroscopy.