A well-struck Keisuke Honda free-kick ended Sevilla's hopes of making their quarter-final debut and secured victory for the well-organised Muscovites to put them into the last eight for the first time since 1992/93.
After a 1-1 draw in Moscow last month, goals from CSKA's Tomas Necid and Sevilla's Diego Perotti had the sides tied at 2-2 on aggregate at the break before Honda's 55th-minute strike flew into the top corner off Sevilla goalkeeper Andres Palop.
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"The players did very well to stop Sevilla getting many clear chances," a beaming CSKA coach Leonid Slutsky told a news conference.
"It's hard to analyse the match much at this early stage but I am very proud that my team has made it through to the quarters."
Sevilla striker Luis Fabiano squandered a chance to put the home side ahead in only the third minute at a noisy Sanchez Pizjuan stadium.
The Brazilian international collected a whipped Jesus Navas cross from the right but hit his first-time shot straight at CSKA goalkeeper Igor Akinfeyev.
The visitors enjoyed plenty of possession in the early stages and lively Japan midfielder Honda forced a smart save from Palop in the 27th minute.
HONDA POWER
Six minutes before the break, a mistake by Serbian defender Ivica Dragutinovic let in Necid, who rifled a low shot into the bottom corner from the edge of the penalty area.
Sevilla were level within two minutes. A long Palop punt bounced through to Navas and he crossed for Perotti to poke the ball past Akinfeyev.
Honda's winner came from a long-range free-kick which Palop failed to deal with as the ball ricocheted into the top corner off the keeper's fists.
Sevilla coach Manolo Jimenez threw on Alvaro Negredo to join fellow strikers Frederic Kanoute and Fabiano but CSKA held firm against some desperate attacking in the final stages as the disconsolate home fans drifted away.
"CSKA were very good in defence and didn't give us many chances on goal," Negredo said in a television interview.
"We managed to get an equaliser in the first half but it was a moment of misfortune in the second half that made it difficult."
Failure for the Andalusians will also put pressure on their budget, after club president Jose Maria del Nido warned before the first leg that missing out on the financial reward for reaching the last eight could push the club into the red.
"All we can do is congratulate them and try to qualify for the competition again," Del Nido said in a television interview.
"We need to focus now on getting third or fourth place in La Liga and we have a great King's Cup final against Atletico Madrid to look forward to which we will try to win."
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