The holders reached the competition's last eight with another professional performance, as Diego Godin and Raul Garcia scored the goals in the second half.
After a 1-1 draw in the first leg in Valencia, the visitors were solid at the back in the opening 45 minutes, as the two sides went to the break locked level.
Godin broke the deadlock six minutes into the second half, though, making the most of poor goalkeeping from Guaita to head his side into the lead.
The Uruguayan defender rose above Antonio Barragan to meet Gabi's corner at the back post after the keeper came off his line but could only flap at the ball.
Atletico substitute Cristian Rodriguez went close to wrapping up the match with an excellent left-foot strike from distance, but Guaita was equal to the task.
But there was still time for Atletico, who sit joint top of La Liga with Barcelona, to score a second goal, as Garcia's glancing header - from another Gabi corner - sealed the result in the 89th minute.
Valencia's Dani Parejo was sent off in stoppage time for kicking the ball away, an offence that saw him given his second yellow card.
The result extended Atletico's unbeaten streak to 17 matches in all competitions.
Racing Santander also won on Tuesday, shocking top-flight outfit Almeria 2-0 on the road.
Third-tier Racing claimed a credible 1-1 draw in the first leg but were expected to be beaten in Almeria.
But after holding firm for the first hour, goals from Mariano Sanz and Ruben Duran saw them claim an unlikely win.
