Dick Advocaat's troops came into the match two points clear of nearest challengers the Republic of Ireland and knowing victory against their unfancied opponents would book their ticket to Poland and Ukraine as Group B winners.
The three points were never in doubt from the moment Alan Dzagoev fired the hosts ahead inside five minutes. A second for Dzagoev and strikes by Sergei Ignashevich and Roman Pavlyuchenko had Russia out of sight at the break, while second-half efforts by Dennis Glushakov and substitute Diniyar Bilyaletdinov added gloss to the scoreline.
The result means Russia top their group on 23 points after seven wins, two draws and one defeat from their 10 qualifiers, while Andorra finish the campaign nursing an unwanted record of 10 straight defeats.
The hosts wasted no time getting their noses in front, Dzagoev firing home sweetly from the edge of the area after Andorra goalkeeper Josep Anton Gomez could only half clear Andrey Arshavin's corner.
Arshavin was again the creator as Russia made it two in the 25th minute, the Arsenal midfielder picking himself after being fouled by Ildefons Lima to deliver a free-kick which was headed home from close range by Ignashevich.
Four minutes later the Russians were out of sight, the Andorran defence again making it far to easy as Glushakov fed Pavlyuchenko from the left and the Tottenham striker had a simple task to fire home low past Gomez.
A one-sided opening period was wrapped up a minute before the interval as Pavlyuchenko turned provider for Dzagoev to nod home from six yards.
It remained one-way traffic after the restart and on 59 minutes the home fans had another goal to celebrate, Pavlyuchenko continuing his fine personal display by sending over an inviting cross which Glushakov met with a thumping header into the top corner.
And the match was put to bed 12 minutes from full-time when Dzagoev fed Bilyaletdinov, the Everton midfielder setting his sights from distance before fizzing a low left-footed shot beyond Gomez.