Luiz put a clutch of the world's most expensive strikers to shame by breaking the deadlock late on before Ramires wrapped up the points in stoppage-time at Stamford Bridge on Sunday.
The win lifted Chelsea above City into third place and back to within nine points of Manchester United with a game in hand, while City are now 10 adrift having played the same number of matches.
Carlos Tevez's groin injury was a huge blow for the visitors and an even bigger boost for their opponents ahead of kick-off. The Argentina striker had been the scourge of Chelsea since leaving Manchester United, scoring four times in three successive victories against them.
Mario Balotelli missed out for very different reasons, despite apologising for the moment of madness that saw him sent off against Dynamo Kiev in the Europa League on Thursday night. Reports of a bust-up with Roberto Mancini may not have helped the striker's cause.
One man who had served his time was Chelsea skipper John Terry, who entered the field to chants of, "There's only one England captain!", with Fabio Capello sat in the stands.
The reinstated defender was a bit slow to close down Yaya Toure in the sixth minute, however, the midfielder given enough space to fire a low 20-yard drive saved well by Petr Cech.
City were on top but Chelsea looked dangerous on the break and wasted a great chance to take a 12th-minute lead when the recalled Salomon Kalou fell over team-mate Ramires as both tried to finish from 12 yards.
That was the cue for the home side to take a grip and they were denied what appeared a clear penalty in the 20th minute when Joleon Lescott handled Kalou's cross.
James Milner, starting for the first time since last month's Manchester derby, earned the game's first yellow card five minutes later after felling Florent Malouda in full flight.
Apart from the early Cech save, neither goalkeeper was being tested, hardly a surprise considering both sides' central strikers had yet to score a Premier League goal for their clubs.
Torres' drought for Chelsea was approaching eight hours and he had not had a sniff on what was his 27th birthday.
That changed in the 34th minute when Kalou presented him with a chance on his left foot from 10 yards, but the Spaniard's lack of confidence was palpable as Nigel de Jong slid in to intercept.
Vincent Kompany then put his body in the way of Frank Lampard's close-range finish.
Kalou almost broke the deadlock three minutes before the break when he brilliantly controlled Malouda's low cross before turning and shooting straight at Joe Hart.
The second half did not start promisingly but when City gifted the ball to Torres in the 51st minute, the striker set up a wonderful, flowing move that Malouda should have finished with a goal instead of sidefooting straight at Hart.
There was concern soon after when Terry stayed down after falling awkwardly.
The reinstated England captain appeared in agony as Capello looked on stony-faced but, following brief treatment, Terry was able to continue.
City came back into the game before De Jong was cautioned for a blatant body check on Essien.
Branislav Ivanovic was unlucky not to give Chelsea a 62nd-minute lead when his point-blank bullet header from Lampard's cross hit Kompany.
Edin Dzeko back-headed Milner's free-kick wide before Ramires was booked for clattering into Aleksander Kolarov.
With 20 minutes, remaining, Torres and Malouda were withdrawn for Didier Drogba and Nicolas Anelka.
Dzeko was booked for a foul on Luiz before Chelsea brought on Yury Zhirkov for Kalou.
A goal immediately followed as Luiz earned a 77th-minute free-kick wide on the left, Drogba whipped the ball in and the Brazilian glanced a header through the fingertips of Hart.
City sent on Adam Johnson for Milner before Barry saw yellow for a foul on Ramires.
Luiz went close to converting another free-kick from Drogba, who became the latest victim of a bookable offence when brought down by Kolarov.
City threw men forward but they were killed off in the second minute of stoppage time when Ramires danced through their defence before clipping beyond Hart.
There was still time for Luiz to blot his copybook with a late caution but the points were already secure.