Luiz broke the deadlock in the 78th minute and compatriot Ramires added a second in stoppage time as Chelsea beat Manchester City 2-0 to ease the pressure on boss Carlo Ancelotti.
Chelsea climbed above City into third in the Barclays Premier League, nine points behind leaders Manchester United with a game in hand.
Kiss of life: Ramires scored a brilliant second to secure a vital win for his under-pressure manager Carlo Ancelotti
Owner Roman Abramovich was at Stamford Bridge to see Luiz score his second goal since signing from Benfica for ?21m in January as Torres again failed to impress and was replaced by Didier Drogba.
Abramovich shook his head as his ?50m striker was hooked 20 minutes from time, but Ancelotti's decision was vindicated when Drogba's free-kick was headed in by Luiz.
The Chelsea boss later confessed he has been lucky to avoid the sack.
Braziliant: David Luiz got the ball rolling for the Blues midway through the second half
He said: 'When their team sleeps for two months, a lot of coaches find themselves at home watching the game on television. I am still here. Fortunately.'
Before kick-off, Chelsea's chief executive Ron Gourlay hinted that Ancelotti was not guaranteed to see out the final year of his three-year deal. 'Let's see where we are at the end of May,' he said.
The Italian did not seem too worried. He said: 'I'm happy in this moment. If one party - the club or myself - is not happy, we'll have to.' And he moved his hands apart.
Top of the flops: Fernando Torres once again struggled to have any sort of positive impact on the side
He said everyone would 'have to be patient' with Torres, who has not scored since his goal for Liverpool at Wolves on January 22.
City boss Roberto Mancini blamed the loss on fatigue from Thursday's Europa League defeat by Dynamo Kiev, when Mario Balotelli was sent off for his kung-fu kick.
He said: 'That game, playing with 10 players, probably affected us.'
Balotelli has been fined two weeks' wages for his red card but came on as a substitute on Sunday.
Carlos Tevez, who was missing with a groin injury, has returned to Argentina but will not be playing for his country. Mancini expects the striker to be fit for City's next match with Sunderland on April 3.
Explore more:People: Didier Drogba, Carlos Tevez, Roman Abramovich, Roberto Mancini, Fernando Torres, Mario Balotelli, Carlo Ancelotti Places: Liverpool, Argentina