Alexander Samedov opened the scoring for Russia in the ninth minute, with Luxembourg defender Chris Philipps trying to stop the ball with his foot but directing it into the net and Viktor Fayzulin doubled the visitors' lead half an hour later.
Denis Glushakov ensured they went into the break with a comfortable lead with a goal on the stroke of halftime, while Alexander Kerzhakov made it four on 73 minutes after being set up by Dmitry Kombarov.
"We played a very good match, with good speed and good desire," Russian media quoted Capello as saying.
"The Luxembourg match is in the past. We got the result we needed, played good football.
"We won because we controlled the ball well, pressed our opponent and didn't let Luxembourg play their game."
Bottom-of-the-table Luxembourg posed little threat for the visitors after their early opener.
Luxembourg goalkeeper Jonathan Joubert got a hand to the second goal, which came after captain Roman Shirokov lofted a perfect pass to Fayzulin and he flicked it home with his left foot.
Russia keeper Igor Akinfeev blocked Daniel Da Mota's shot shortly before the break and his side put the match out of reach in the second minute of first-half stoppage time when the ball fell to midfielder Glushakov who pushed a shot past Joubert.
Kerzhakov's second-half goal was the icing on the cake and came shortly after Luxembourg had missed a tantalising chance when Stefano Bensi passed the ball across the goal only to watch in disappointment as none of his team mates could drive it home.
The match was briefly interrupted around the 80th minute when a fan ran onto the field and dived into one of the goals before security guards escorted him off the pitch.
(Writing by Steve Gutterman; Editing by Sonia Oxley/Greg Stutchbury)
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