Background: The COVID-19 pandemic had a massive impact on healthcare systems, increasing the risks of psychological distress in health professionals. Burnout is a prolonged response to chronic emotional and interpersonal stressors on the job and is defined by the three dimensions of emotional exhaustion, cynicism, and personal inefficacy. Methodology: A cross-sectional descriptive design was used to assess the burnout and resilience among frontline nurses in the emergency department of a tertiary care center in North India during COVID-19 pandemic. The sample consisted of 120 frontline nurses working in the emergency department, selected by a simple random sampling method. Data were collected using the Maslach burnout inventory-general survey and the Connor–Davidson Resilience Scale. Results: The nurses in the emergency during pandemic experienced a moderate-to-severe level of burnout in emotional exhaustion (29.13 ± 10.30) and depersonalization (12.90 ± 4.67) but mild-to-moderate level of burnout in reduced personal accomplishment (37.68 ± 5.17) and showed a moderate to a high level of resilience (77.77 ± 12.41). The two metrics of burnout viz., emotional exhaustion and personal inefficacy had a significantly negative correlation with resilience among the frontline nurses in the emergency (r = 0.25, p < 0.05 and r = 0.31, p < 0.01, respectively). A significant negative correlation has been identified between burnout and resilience that informs the role of resilience in alleviating burnout during this pandemic. Conclusion: Effective interventions for improving resilience are needed to relieve nurses’ burnout and workplace stressors. Also, the administration should ensure a healthy workplace and adopt a positive attitude and harmonious relationship with the frontline workers in the mitigation of the pandemic.