A vehicle powertrain has an engine, a driving shaft having a passage defined therein, a driven shaft, a pump, a hydraulic fluid reservoir, and a CVT. A driving pulley of the CVT includes a fixed sheave and a movable sheave disposed on the driving shaft for rotation therewith, a spring biasing a movable sheave away from the fixed sheave, and a CVT chamber fluidly communicating with the passage of the driving shaft. The pump supplies hydraulic fluid from the reservoir to the passage in the driving shaft. The hydraulic fluid flows from the passage to the CVT chamber to create a hydraulic pressure in the CVT chamber. The hydraulic pressure in the CVT chamber biases the movable sheave toward the fixed sheave.