The turbine of an automobile turbocharger commonly operates under pulsating inflow, which leads to an undesired “hysteresis” performance. This study is to investigate this phenomenon by presenting a computational flow analysis that can capture the pulsating flow physics in a turbocharger turbine. We use a method of higher-order accuracy, and the key techniques include: (i) the Space–Time Variational Multiscale (ST-VMS) method, which is a stabilized formulation and a turbulence model, (ii) the ST Slip Interface (ST-SI) method, which maintains the solution quality near rotor surface, (iii) the Isogeometric Analysis (IGA), where we use NURBS basis functions in space and time, and (iv) weakly-imposed Dirichlet boundary conditions, which can give accurate mean flow solutions on a coarse mesh with unresolved boundary layers. The geometric model is from a realistic turbocharger turbine. The pulsating inflow conditions are taken from a 1D engine-cycle simulation. The computations are carried out with an incompressible-flow solver. The results show that the turbine is likely to operate far from nominal conditions under pulsating inflow, and geometric features such as exhaust manifold and vanes play a significant role in improving the performance. The techniques show a good potential for solving difficult turbomachinery problems.