A powertrain control apparatus controls a powertrain including a lock-up clutch, and an engine, in which fuel supply is cut off, directly to an automatic transmission. The control apparatus includes a control unit that controls the engine so that fuel supply resumes in the engine and a setting unit that sets a hydraulic-pressure instruction value based on a temperature of a combustion chamber of the engine so that a time required to discharge the lock-up clutch is longer when the temperature of the combustion chamber is a first temperature than when the temperature of the combustion chamber is a second temperature which is higher than the first temperature, when the lock-up clutch is controlled to be brought to the disengaged state from the engaged state and the fuel supply to the engine is resumed. The lock-up clutch is then operated by hydraulic pressure corresponding to the hydraulic-pressure instruction value.