The current work presents a computationally cost-effective numerical model that successfully simulates a heat pump water heater (HPWH) under typical working conditions of dwellings. The model’s main components are a stratified tank and the heat-pump unit. Both systems are coupled, since a good prediction of water temperature is needed to accurately predict the heat-pump performance. Ten thermocouples measured the tank wall temperature. Measurements and simulations were performed under challenging conditions of a heavy stratification. The 190 L tank stratification was successfully modeled employing a 1D model, experimentally adjusted by three tapping cycles, with 6 × 22, 6 × 33, and 3 × 33 L consumptions, covering flowrates of 4 and 6 L/min. Water temperature is obtained with an uncertainty of 2.6 °C while the heat-pump was ON. A black box model has been used to obtain the heat-pump performance out of the external and condenser temperatures. For the analyzed days, the COP estimation presents an uncertainty of only 5.1%. Finally, an application example is included. It was used to simulate six tapping cycles of the European standard for heat pump water heaters testing (EN 16147). The results show the possibilities for heat-pump manufacturers of applying this calibrated model to predict the performance of HPWHs under different conditions.