A vehicle includes a power plant, continuously variable transmission (CVT), drive wheels, sensors, and controller. The CVT achieves a fixed gear/positive engagement and friction drive modes, and includes an input member that receives input torque from the power plant, an output member, and a variator assembly having drive and driven variator pulleys. The pulleys are connected to each other via an endless rotatable drive element, and to a respective one of the input and output members. Pulley actuators change a CVT speed ratio. The controller calculates a relative slip of the pulleys using measured speeds and displacements from the sensors, reduces the relative slip until the relative slip is below a calibrated speed limit or within a calibrated speed range via actuator control signal to the pulley actuators, and commands the fixed gear/positive engagement mode via positive engagement control signals to the CVT until the relative slip reaches zero.