Goals from Yury Gazinsky, Artem Dzyuba and Aleksandr Golovin helped them on their way, but the former Real Madrid man stole the limelight after coming on as a first half substitute.
After an opening ceremony which included British pop icon Robbie Williams, it took just 12 minutes for the tournament’s first goal, with Gazinsky opening his international account with a well-taken header across goal.
Cheryshev, Dzagoev’s replacement, doubled their lead with a fine finish to complete a good attacking move.
Villarreal winger Cheryshev took the ball on inside the box, taking two sliding Saudi Arabia players out of the game with his first touch before getting the ball out of his feet and firing high into the net.
After a slow start to the second half, substitute Dzyuba netted with his first touch on 71 minutes, with an impressive header from close range.
Cheryshev got his second late on, with a sublime outside-of-the-boot finish before Golovin added a fifth deep into stoppage time with a 20-yard free-kick.