Background and Objectives: Serum albumin is a widely available and inexpensive biomarker that reflects nutritional status and physiological reserve. Hypoalbuminemia has been linked to poor postoperative outcomes in surgical oncology; however, its role in predicting early complications after cytoreductive surgery for ovarian cancer, as well as the potential contribution of systemic inflammatory indices in nutritionally preserved patients, remains incompletely understood. This study aimed to evaluate the predictive value of early postoperative serum albumin for early surgical complications and to explore whether inflammatory indices could offer additional prognostic information in patients with adequate albumin levels. Materials and Methods: We conducted a retrospective observational cohort study including patients undergoing cytoreductive surgery for ovarian cancer at two Italian tertiary referral centers between July 2023 and December 2025. Postoperative serum albumin was measured on the first postoperative day. Systemic inflammatory parameters were assessed using perioperative changes in neutrophils and composite indices. Early postoperative complications occurring within 30 days were recorded. Multivariable logistic regression analyses were performed, and subgroup analyses were conducted in patients with postoperative albumin ≥3 g/dL. Receiver operating characteristic (ROC) analysis was used to identify an optimal cutoff for significant inflammatory predictors. Results: A total of 121 patients were included, of whom 30 developed early postoperative complications. Patients with complications had significantly lower postoperative albumin levels than those without complications (median 2.75 vs. 3.09 g/dL; p < 0.001). In multivariable analysis, lower postoperative albumin independently predicted early complications (OR 0.26, 95% CI 0.06–0.86). In the subgroup of patients with preserved albumin levels (≥3 g/dL), a smaller postoperative neutrophil decline independently predicted complications (OR 1.56, 95% CI 1.12–2.70). A neutrophil drop cutoff of −1.15 × 103/dL showed good specificity (81.5%) and high negative predictive value (95.7%). Conclusions: Early postoperative serum albumin is a strong predictor of early surgical complications after cytoreductive surgery for ovarian cancer. In patients with preserved nutritional status, dynamic neutrophil changes provide additional prognostic information. Incorporating low-cost metabolic and inflammatory biomarkers may enhance early postoperative risk stratification and support more personalized patient management.