Background: Hematological indices can predict disease severity, progression, and death in patients with coronavirus disease-19 (COVID-19). Objectives: To study the predictive value of the dynamic changes (first 48 h after ICU admission) of the following ratios: neutrophil-to-lymphocyte (NLR), platelet-to-lymphocyte (PLR), monocyte-to-lymphocyte (MLR), systemic inflammation index (SII), and derived neutrophil-to-lymphocyte (dNLR) for invasive mechanical ventilation (IMV) need and death in critically ill COVID-19 patients. Methods: Observational, retrospective, and multicentric analysis on 272 patients with severe or critical COVID-19 from two tertiary centers. Hematological indices were adjusted for confounders through multivariate analysis using Cox regression. Results: Patients comprised 186 males and 86 females with no difference across groups (p > 0.05). ΔNLR > 2 had the best independent predictive value for IMV need (HR = 5.05 (95% CI, 3.06–8.33, p < 0.0001)), followed by ΔSII > 340 (HR = 3.56, 95% CI 2.21–5.74, p < 0.0001) and ΔdNLR > 1 (HR = 2.61, 95% CI 1.7–4.01, p < 0.0001). Death was also best predicted by an NLR > 11 (HR = 2.25, 95% CI: 1.31–3.86, p = 0.003) followed by dNLR > 6.93 (HR = 1.89, 95% CI: 1.2–2.98, p = 0.005) and SII > 3700 (HR = 1.68, 95% CI: 1.13–2.49, p = 0.01). Conclusions: Dynamic changes of NLR, SII, and dNLR independently predict IMV need and death in critically ill COVID-19 patients.