Sneijder, who will play a key role for the Netherlands at the World Cup finals in South Africa, fired the Italians ahead less than six minutes into the game when his low 20-metre free-kick skidded under CSKA's defensive wall and evaded goalkeeper Igor Akinfeyev.
With Inter holding a 1-0 lead from the first leg, Sneijder's goal all but killed the home team's chances as the Italian champions held firm for a comfortable 2-0 win on aggregate.
CSKA's Nigerian defender Chidi Odiah was sent off in the 49th minute after he picked up his second yellow card after a foul on Samuel Eto'o.
Asked by Reuters if the game plan was to strike early, Inter coach Jose Mourinho said: "The plan was to score before them.
"In the first leg we had 10 shots before scoring, today we scored on our first shot and the tie is in the pocket. After that, the game was easy to control," he added.
"You could see emotionally the CSKA players were down after giving up that goal and we just had to control the tempo."
CSKA coach Leonid Slutsky conceded the early goal effectively settled the tie.
"We prepared a whole system how to play them," Slutsky, dubbed the "Russian Mourinho" by local media for his tactical approach, told a news conference. "But it was all out the window when they scored after just six minutes."
THREE-PRONGED ATTACK
Mourinho started Tuesday's game with the same three-pronged attack, consisting of Eto'o, Diego Milito and Goran Pandev, with Sneijder just behind them, just like he did against Chelsea in the return leg of the previous round in London, where Inter also won 1-0.
Sneijder's participation had been in doubt after he hurt his left ankle in Monday's training, while Inter's Brazilian central defender Lucio was back in the starting line-up after being suspended for the first leg.
His midfield compatriot Thiago Motta was missing due to a thigh injury.
Meanwhile CSKA, already without suspended midfielders Milos Krasic and Yevgeny Aldonin, also lost central defender Vasily Berezutsky early in the first half with a thigh injury.
But after a nervous opening, the Russians finally got into the game and Czech forward Tomas Necid had the first real opportunity for the hosts midway through the first half but his low strike from the edge of the box just missed the far post.
CSKA playmaker Alan Dzagoyev also wasted an excellent chance just after half hour and Inter nearly doubled the lead right after but Akinfeyev made a fine stop from Milito's close-range strike.
With CSKA having to score three times to progress, their chances all but disappeared after they were reduced to 10 men early in the second half and the game soon lost its intensity.
Inter keeper Julio Cesar had to make a great diving save from Mark Gonzalez's powerful drive to protect a clean sheet, while at the other end Akinfeyev again denied on-rushing Milito.
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