A vehicle includes an air-conditioning (AC) compressor, an engine, a belt-integrated starter generator (BISG), and a controller. The controller, responsive to detecting a first AC compressor engagement condition, compares a first AC torque demand that is required to engage the AC compressor with an available torque from the BISG. The controller further, responsive to the available torque being insufficient to engage the AC compressor, engages the AC compressor using the available torque from the BISG and an engine torque from the engine to compensate a torque shortfall between the AC torque demand and the available torque by retarding spark timing and increasing air intake.