An internal combustion engine includes a cylinder block defining a cylinder, a cylinder head, an intake valve, an exhaust valve, and a variable exhaust valve timing mechanism. The engine also includes a turbocharging system configured to pressurize ambient airflow for delivery to the cylinder. The turbocharging system includes a low-flow turbocharger, a high-flow turbocharger, and a flow control device for selectively directing post-combustion gas to the low-flow and high-flow turbochargers. A controller directs the post-combustion gas to the low-flow turbocharger and selects a first predetermined exhaust valve timing when the engine operates below a predetermined speed and above a predetermined load. Alternatively, the controller directs the post-combustion gas to the high-flow turbocharger and selects a second predetermined exhaust valve timing at or above the predetermined engine speed. The first predetermined exhaust valve timing traps less post-combustion gas in the cylinder as compared to the second predetermined exhaust valve timing.