Alan Dzagoev, who scored the only goal in a pivotal 1-0 away win over Slovakia on Friday, led the way with a first-half double while Sergei Ignashevich and Roman Pavlyuchenko struck to make it 4-0 before the break.
The Russians, who needed only a draw against the rank outsiders Andorra to stay ahead of Ireland at the top of the group, added two more through Denis Glushakov and substitute Diniyar Bilyaletdinov after the interval.
"We wanted not just to win and clinch a Euro 2012 place but win big to make our fans happy," Dzagoev told Russian television.
The CSKA Moscow playmaker opened his account in the fifth minute and also fired a superb volley on the turn into the far corner just before half-time.
Ignashevich headed an Andriy Arshavin free-kick for Russia's second in the 26th minute before Pavlyuchenko made it 3-0 four minutes later.
It was Pavlyuchenko's 20th goal in 45 internationals while Glushakov scored his first for Russia just before the hour.
Bilyaletdinov completed the rout with a low strike six minutes after coming on for Igor Semshov.
Russia coach Dick Advocaat, who took over in 2010, praised his team for reaching the finals.
"It was a very difficult qualifying campaign but from the start I was sure that we would qualify for the finals. I think we deserved to finish first," the Dutchman told reporters.
"I hope that from now on, our team will not be criticised as much as it was in the past.
"With all the respect to Andorra we knew that we just couldn't lose to them and I think today we scored the biggest win of all in our group."
Andorra's mostly amateur side rarely threatened Russia goalkeeper Vyacheslav Malafeyev, who only had to make one stop in the entire match.
The world's joint lowest-ranked team lost all their 10 matches in the group, conceding 25 and scoring just once.
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