Atletico were only able to come away from last month's first leg with a 1-1 draw, but they never looked in danger of being on the end of an upset at the Wanda Metropolitano, with Torres scoring twice in a strong performance.
Diego Simeone refused to jeopardise progression by playing an inexperienced team like he did in the away leg and his side looked focused as a result in making it four wins from their last five games.
Initially they wasted opportunities and began to look frustrated, but Jose Maria Gimenez finally ended Elche's resistance with a header at the back post in the 31st minute.
And their second followed shortly after, with Torres producing a fine finish for his first goal at the Wanda Metropolitano.
The chances continued to flow for Atleti and although wasteful finishing again surfaced after the break, Torres finally doubled his tally in the 68th minute to make absolutely sure of their qualification for the last 16.
2 - Fernando Torres has become the first player to score a brace at Wanda Metropolitano and was the last player to score a brace at Vicente Calderon (all competitions). Idol. pic.twitter.com/aku0uFXvql — OptaJose (@OptaJose) November 29, 2017
Atletico were quick out of the blocks and almost broke the deadlock after just three minutes, but Luciano Vietto – enjoying a rare start – shot just wide of the left-hand post from a tight angle after a fine run in from the right flank.
Elche had to rely on the post to save them just before the half-hour mark, with Koke's 30-yard drive smacking against the frame of the goal.
But there was to be no denying Gimenez soon after, however, as the Uruguay defender stealthily appeared behind the Elche defence at a corner and headed just inside the right-hand post.
And with their very next attack, Atleti added a second.
Guille Vallejo failed to hold on to Yannick Carrasco's long-range effort and Torres was there to pounce on the rebound, tucking in from a tight angle.
The wasteful Vietto should have extended the lead just before the break, but he fired over from the centre of the box after Torres' cut-back.
Things were similarly one-sided after the break and Atletico should have gone three up shortly after the restart, but Nicolas Gaitan could only find the side-netting after a fine flowing move.
Atletico then began to sit back a little more and invite pressure in the hope of catching Elche on the break.
And they almost did so in the 64th minute, as Gaitan darted in from the left, skipped past a couple of challenges and fed Thomas Partey into the right side of the area, only for his squared pass to be cut out at the last moment.
An even better chance fell to Torres soon after, with Vietto teeing him up with an easy finish from 12 yards, yet he inexplicably scuffed wide.
He made amends a few moments later, though, slamming past Vallejo from close range after being released by substitute Sime Vrsaljko.
Torres almost got his hat-trick 10 minutes from the end, but Vallejo made a brilliant save down to his right to deny the striker, as in-form Atletico settled for a three-goal victory.