Background: The purpose of this study was to investigate how the systemic inflammation response index (SIRI), systemic immune-inflammation index (SII), neutrophil/lymphocyte ratio (NLR) and platelet/lymphocyte ratio (PLR), and radiomic metrics (quantitative descriptors of image content) extracted from MRI sequences by machine learning increase the efficacy of proper presurgical differentiation between benign and malignant salivary gland tumors. Methods: A retrospective study of 117 patients with salivary gland tumors was conducted between January 2015 and November 2022. Univariate analyses with nonparametric tests and multivariate analyses with machine learning approaches were used. Results: Inflammatory biomarkers showed statistically significant differences (p < 0.05) in the Kruskal–Wallis test based on median values in discriminating Warthin tumors from pleomorphic adenoma and malignancies. The accuracy of NLR, PLR, SII, and SIRI was 0.88, 0.74, 0.76, and 0.83, respectively. Analysis of radiomic metrics to discriminate Warthin tumors from pleomorphic adenoma and malignancies showed statistically significant differences (p < 0.05) in nine radiomic features. The best multivariate analysis result was obtained from an SVM model with 86% accuracy, 68% sensitivity, and 91% specificity for six features. Conclusions: Inflammatory biomarkers and radiomic features can comparably support a pre-surgical differential diagnosis.