A power system for use with an engine having at least one cylinder, and a piston, a fuel injector, and an exhaust valve associated with the at least one cylinder, is disclosed. The power system may have an exhaust passage, an aftertreatment component disposed within the exhaust passage, and a valve actuator configured to selectively move the exhaust valve. The power system may also have a controller in communication with the fuel injector and the valve actuator. The controller may be configured to make a determination to heat the aftertreatment component, to activate the valve actuator to hold open the exhaust valve as the piston moves through a top-dead-center position to disable the at least one cylinder based on the determination, and to activate the fuel injector to inject fuel into the at least one cylinder while the at least one cylinder is disabled.