A study of Argentine wines was carried out by direct injection of the samples without previous treatment in a high-performance liquid chromatography system coupled to a diode array detector (HPLC-DAD). The collected data, corresponding to six different varietals (Bonarda, Cabernet Sauvignon, Malbec, Merlot, Syrah, and Tempranillo), were processed with a new chemometric approach: determining the fractal dimension of principal components or fractal dimension analysis (FDA). A comparative study of the efficiency of the new proposed model to discriminate wine samples according to botanical origin was made with methods based on a linear multivariate resolution curve-alternating least squares model (MCR-ALS) previously reported. The results show that the fractal dimension analysis of the data improves the discrimination between all the varietals studied, allowing better discrimination in relation to other reported methodologies. Finally, a comparative analysis of the method’s sustainability was carried out using the Analytical Eco-Scale indicator. This analysis demonstrated that the method based on fractal analysis is a simple procedure that meets most of the Green Analytical Chemistry requirements.