Chelsea had to overturn a 1-0 first-leg deficit to progress and levelled the tie through Juan Mata after 33 minutes, only for Vlad Chiriches to score on the stroke of half-time when the Blues failed to clear a corner.
The away goal meant Chelsea needed to score twice to be included in tomorrow's last-eight draw and captain John Terry headed in after 58 minutes and Torres netted after 71 minutes to seal victory - before the Spaniard hit the bar with an 87th-minute penalty.
Torres' strike was the £50million striker's second goal in 19 games - the effort at Middlesbrough which ricocheted in off his back was belatedly credited to Ramires - and his reward was a nosebleed sustained soon afterwards.
It was a crucial strike from the much-maligned Spaniard and means Chelsea, who play West Ham in the Barclays Premier League on Sunday, now face four games in nine days, beginning against Southampton on Easter Saturday.
Boss Rafael Benitez made four changes for Chelsea's 52nd match of a season which could feature 70 games - if the Blues advance to the finals of the Europa League and the FA Cup.
Terry, Torres, John Obi Mikel and Eden Hazard were included following the 2-2 draw at Manchester United.
Chelsea's last home defeat in European competition was to United - two years ago in the Champions League quarter-finals - and they were hoping to carry the momentum from the second half of last Sunday's Old Trafford encounter.
It was Raul Rusescu's penalty which handed Steaua the advantage at the end of the first leg and the striker nearly doubled their overall lead after 12 minutes.
Mikel dithered over a clearance and Cristian Tanase stole the ball before finding Rusescu, who breached the offside trap before his shot was saved by Petr Cech.
After a quick Mata free-kick was held by Ciprian Tatarusanu, Steaua captain Alexandru Bourceanu fired a 30-yard warning shot narrowly wide and Cech saved from Tanase, who was causing Terry, in particular, problems with his pace.
When the hosts took the direct route it paid off.
Mata picked up the ball inside the Steaua half in the right channel and ran at his marker.
The Spaniard played the ball inside to Ramires, who continued running at the defence before playing a return pass.
While Torres moved out of the way, Mata used his body to shield the ball from Iasmin Latovlevici and his shot squirmed in under Tatarusanu.
Torres shot narrowly wide soon after before Mata and Hazard crafted an opening, only for the Belgian's shot to be saved.
Chelsea still could not relax, though, as Ashley Cole had to be alert to halt Adrian Popa after David Luiz had given the ball away.
From the resulting corner and the last move of the first half, Steaua restored their advantage.
The set-piece was played to the near post and a scramble ensued inside the six-yard box, with Tanase's shot smartly saved by Cech, who could do nothing about the rebound as Chiriches fired into the roof of the net.
Chelsea needed two goals in the second half and the first came after Cornel Rapa fouled Hazard.
Mata delivered towards Terry. The skipper's powers may have been reduced by age and niggling injury, but when left unmarked he remains a potent force and his header from 10 yards went in off the post.
Cech saved a dipping shot from Alexandru Chipciu before Mata set up the third goal Chelsea needed. He cut in from the right, Hazard stepped over the left-footed cross and Torres picked up the ball.
The striker, whose most recent prior strike was at Brentford in the FA Cup, stepped around Lukasz Szukata and netted low across goal.
The World Cup winner lost his footing in the area soon after under the challenge of Szukata, emerging with a bleeding nose, before shooting narrowly wide.
Chelsea were awarded a penalty when Hazard was caught by Bourceanu. Torres stepped up and sent the goalkeeper the wrong way - but his shot hit the top of the crossbar.
Fortunately for the hosts he had already done enough to secure a place in the quarter-finals.