Energy carried by engine exhaust pulses is critical to the performance of a turbine or any other exhaust energy recovery system. Enthalpy and exergy are commonly used concepts to describe the energy transport by the flow based on the first and second laws of thermodynamics. However, in order to investigate the crank-angle-resolved exhaust flow enthalpy and exergy, the significance of the flow parameters (pressure, velocity, and temperature) and their demand for high resolution need to be ascertained. In this study, local and global sensitivity analyses were performed on a one-dimensional (1D) heavy-duty diesel engine model to quantify the significance of each flow parameter in the determination of exhaust enthalpy and exergy. The effects of parameter sweeps were analyzed by local sensitivity, and Sobol indices from the global sensitivity showed the correlations between each flow parameter and the computed enthalpy and exergy. The analysis indicated that when considering the specific enthalpy and exergy, flow temperature is the dominant parameter and requires high resolution of the temperature pulse. It was found that a 5% sweep over the temperature pulse leads to maximum deviations of 31% and 27% when resolving the crank angle-based specific enthalpy and specific exergy, respectively. However, when considering the total enthalpy and exergy rates, flow velocity is the most significant parameter, requiring high resolution with a maximum deviation of 23% for the enthalpy rate and 12% for the exergy rate over a 5% sweep of the flow velocity pulse. This study will help to quantify and prioritize fast measurements of pulsating flow parameters in the context of turbocharger turbine inlet flow enthalpy and exergy analysis.