A power system has a prime mover. The power system may also include a multiple-ratio transmission having a rotary input member and a rotary output member. Additionally, the power system may include a coupler connected between the prime mover and the rotary input member of the multiple-ratio transmission. The power system may also include an electric machine. Additionally, the power system may include power-system controls operable to automatically control whether the rotary input member of the multiple-ratio transmission is drivingly connected to the prime mover, including automatically controlling whether the coupler has a power-transmitting operating state. The power-system controls may also be configured to operate the electric machine to reduce the speed of the prime mover in concert with an upshift of the multiple-ratio transmission.