The Spanish internationals' strikes helped holders Barca defeat second division leaders Racing to progress from a surprisingly tight last 16 clash and record an 11th consecutive victory across all competitions.
The hosts had two goals disallowed for offside, and record 32-time winners Barca did just enough to claim victory.
Having seen Real Madrid eliminated at second-tier Albacete on Wednesday, Barca coach Hansi Flick named a fairly strong side, including teenage star Yamal.
After a 15-minute delay with some fans stuck outside, the match kicked off at Racing's Sardinero stadium, and Barca quickly took control of the ball.
The Catalans struggled to turn possession into a meaningful opening, though, and when they finally did, Dani Olmo missed his kick from Marcus Rashford's dangerous cross.
Racing looked to breach Barcelona's high defensive line, but when they did get in behind, the visitors managed to mop up well.
Giorgi Guliashvili's low effort from range was fielded comfortably by Joan Garcia, and that was as close as the hosts came.
Barcelona continued to push forward in the second half, and Rashford had a shot tipped away and also drilled narrowly wide.
Eventually, the Spanish champions took the lead through Torres, after Fermin Lopez sent him through on goal. The Spain international rounded Racing goalkeeper Jokin Ezkieta and rolled home.
The hosts were forced on the offensive and twice had the ball in Barcelona's net, but both of Manex Lozano's goals were ruled out for offside.
Barca goalkeeper Garcia made a superb save to thwart Lozano one-on-one deep in stoppage time and avoid the game going to extra time.
Barca wrapped up their win with the last kick of the match, Yamal tapping in Raphinha's cross at the back post.
Elsewhere, Valencia won 2-0 at Burgos to reach the last eight.
Check out the match stats from the Barcelona win with Flashscore.