In the presented work, a three-way analysis of ultra-performance liquid chromatography-photodiode array (UPLC-PDA) dataset was performed by parallel factor analysis (PARAFAC) for quantitatively resolving a ternary mixture containing paracetamol and methocarbamol with indapamide selected as an internal standard in their co-eluted chromatographic conditions. Paracetamol and methocarbamol were quantified in the working range between 3–24 and 5–50 μg/mL by applying PARAFAC decomposition to UPLC-PDA data array obtained under unresolved chromatographic peak conditions. To compare the experimental results provided by co-eluted UPLC-PARAFAC method, an ordinary UPLC method was developed ensuring proper separation of the peaks. The performance of both PARAFAC and ordinary UPLC methods were assessed by quantifying independent test samples, intra- and inter-day samples and spiked samples of pharmaceutical preparations. Then, both methods were applied for quantitative estimation of the related drugs in a commercial pharmaceutical preparation. In this study, PARAFAC method was proved to be a very powerful alternative for the quality control of pharmaceutical preparations containing paracetamol and methocarbamol even in their co-eluted chromatograms with high precision and accuracy in a short chromatographic runtime of 1.2 min.