The table-toppers met no resistance from Koldo Alvarez' men as they dismantled the visitors in an impressive style
Dick Advocaat's men dominated from start to finish as they secured first spot in Group B ahead of second-placed Ireland.
Alan Dzagoev was the first to get on the scoresheet as in the fifth minute he sent a vicious shot in the left corner from inside the penalty area, to give Advocaat's players a one-goal cushion early in the game.
Just before the half-hour mark, Russia hit Andorra with a three-minute double salvo as Sergei Ignashevich made it two with a powerful header from inside the six-yard box, and then Roman Pavlyuchenko made it three, finishing in the right corner with a precise shot.
The Tottenham striker played an important part in the fourth goal as well, as moments before half-time he produced a superb cross from the left wing, which Dzagoev headed past Josep Gomes.
Russia continued to dominate after the break, and added a fifth on the hour mark through Denis Glushakov, who scored with a superb header, following a pass by Pavlyuchenko.
Diniyar Bilyaletdinov put the icing on the cake with another strike in the 78th minute to complete the rout as Russia head to Poland and Ukraine, leaving Republic of Ireland in the play-off position.