COVID-19 and dengue disease are challenging to tell apart because they have similarities in clinical and laboratory features during the acute phase of infection, leading to misdiagnosis and delayed treatment. The present study evaluated peripheral blood cell count accuracy to distinguish COVID-19 non-critical patients from non-severe dengue cases between the second and eleventh day after symptom onset. A total of 288 patients infected with SARS-CoV-2 (n = 105) or dengue virus (n = 183) were included in this study. Neutrophil, platelet, and lymphocyte counts were used to calculate the neutrophil–lymphocyte ratio (NLR), the platelet–lymphocyte ratio (PLR), and the neutrophil–lymphocyte*platelet ratio (NLPR). The logistic regression and ROC curves analysis revealed that neutrophil and platelet counts, NLR, LPR, and NLPR were higher in COVID-19 than dengue. The multivariate predictive model showed that the neutrophils, platelets, and NLPR were independently associated with COVID-19 with a good fit predictive value (p = 0.1041). The neutrophil (AUC = 0.95, 95% CI = 0.84–0.91), platelet (AUC = 0.89, 95% CI = 0.85–0.93) counts, and NLR (AUC = 0.88, 95% CI = 0.84–0.91) were able to discriminate COVID-19 from dengue with high sensitivity and specificity values (above 80%). Finally, based on predicted probabilities on combining neutrophils and platelets with NLR or NLPR, the adjusted AUC was 0.97 (95% CI = 0.94–0.98) to differentiate COVID-19 from dengue during the acute phase of infection with outstanding accuracy. These findings might suggest that the neutrophil, platelet counts, and NLR or NLPR provide a quick and cost-effective way to distinguish between dengue and COVID-19 in the context of co-epidemics in low-income tropical regions.