Gonzalo Higuain and Karim Benzema were also on target for Jose Mourinho's side in the second leg of the last-16 tie after the first leg ended 1-1 in Moscow last month.
CSKA midfielder Zoran Tosic netted a memorable goal 13 minutes from time but it was no more than a consolation for the Russian team, who had their chances to make life a bit more uncomfortable for the home side only to be ultimately undone by their own sloppy errors.
Leonid Slutsky's side had never lost a European match against Spanish opposition, winning three and drawing three. This was a first defeat, but they were always in the match despite going down 5-2 on aggregate.
Mourinho commented later that he felt his side had switched off when they moved 3-0 ahead.
Certainly, the match could have taken on a different complex had Seydou Doumbia not lifted a shot over the bar from Alan Dzagoev's delightful pass on seven minutes with Ahmed Musa just failing to provide Doumbia with a finish from a fine run and cross five minutes later.
Kaka drilled a shot wide from Ronaldo's cutback before Higuain converted the opener on 24 minutes when he slipped the ball into the unguarded net after fine play involving Sami Khedira and Kaka.
Home goalkeeper Iker Casillas was forced to nudge the ball over his bar on 32 minutes from Musa's shot before Real grabbed their second goal of the evening on 55 minutes.
This time Ronaldo unloaded a shot from 35 yards out. The ball dipped and swerved in the air as the unfortunate CSKA goalkeeper Sergey Chepchugov missed the flight of the ball as it somehow wound up in the net.
Doumbia clipped an effort wide with Casillas grounded on 68 minutes. That miss proved fatal with substitute Benzema scoring with only this third touch of the ball after replacing Higuain as he stabbed the ball home with Chepchugov failing to hold his initial shot.
Tosic showed his class by leaving Pepe for dead to thump a shot in off Casillas's bar from distance, but Ronaldo rounded off the scoring deep into injury time when Pepe bounded forward to feed Benzema who crossed for Ronaldo to tap into the unguarded net.
The draw for the quarter-finals and semi-finals is made on Friday with Real joining Barcelona, AC Milan, Bayern Munich, Benfica, Marseille, Chelsea and APOEL Nicosia in the pot.