The COVID-19 pandemic had a considerable impact on the whole health sector, particularly on emergency services. Our aim was to examine the performance of the Hungarian National Ambulance Service during the first four waves of the pandemic. We defined the 2019 performance of the service as the baseline and compared it with the activity during the pandemic years of 2020 and 2021. The data contained deliveries related to acute myocardial infarction, hemorrhagic stroke, ischemic stroke, overall non-COVID-related ambulance deliveries, COVID screenings performed by the ambulance service, and COVID-related ambulance deliveries. The data were aggregated for each week of the investigated time period and stratified by gender and age. Compared with the pre-pandemic era, we found a significant increase in all three medical conditions and overall deliveries (p < 0.001 in all cases). As a result of the increased burden, it is important for emergency services to prepare for the next global epidemic and to improve organizational performance and rescue activities. The Hungarian example highlights that in a pandemic, it can be beneficial to organize the emergency care of a country or a larger region under a single provider with a single decision maker supported by business intelligence.