In a control system and a control method, an electronic control unit is configured to crank an engine by setting a clutch to a half engaged state in a state where operation of the engine is stopped during traveling. The half engaged state is a state where the clutch is engaged with a slip. The electronic control unit is configured to, after a rotation speed of the engine has reached an ignition permission rotation speed or higher, increase a transmitted torque capacity of the clutch to a transmitted torque capacity that satisfies the following conditions i) and ii): i) the transmitted torque capacity is larger than a transmitted torque capacity before the rotation speed of the engine has reached the ignition permission rotation speed; and ii) the transmitted torque capacity allows the clutch to be kept in the half engaged state.