(1) Background: Severe coronavirus disease can be complicated by a hypercoagulable state in conjunction with sepsis, increasing the risk of venous thromboembolism. This study aimed to observe the effect of anticoagulants on 30-day high-dependency unit (HDU) outcomes of moderate to severe coronavirus disease 2019 (COVID-19) patients of a tertiary care hospital at Rawalpindi, Pakistan. (2) Methods: A retrospective propensity-based case–control study was carried out to examine COVID-19 patients admitted to the HDU. Patient groups who did and did not receive anticoagulants were labeled as “anticoagulant” and “non-anticoagulant”, respectively. Case–control matching (1:1) was performed via propensity scores (calculated by a regression model). Kaplan–Meier and logrank analyses were used to study survival probability. Single predictors of outcomes were determined by Cox regression analysis. (3) Results: The anticoagulant group had elevated D-dimers, advanced age, more comorbidities and a higher frequency of severe disease compared to the non-anticoagulant group (p < 0.05). Therefore, 47 cases and 47 matched controls were selected based on their propensity scores. The primary endpoint was outcome (survived vs. died). The 30-day in-HDU mortality was 25.5% for cases and 61.7% for controls (p = 0.0004). The median time from admission to death was 16 days for the case group and 7 days for the control group (p < 0.0001). The 30-day mortality was 19.1% for the enoxaparin group and 16.4% for the heparin group (p > 0.05). Enoxaparin (therapeutic and prophylactic doses) and heparin (prophylactic dose) were found to be independent factors affecting the outcomes of these patients (p < 0.001). (4) Conclusions: Anticoagulants play a beneficial role in reducing mortality among COVID-19 patients. Both anticoagulant formulations, enoxaparin (therapeutic and prophylactic doses) and heparin (prophylactic dose), were associated with improving survival among these patients.