Once again Chelsea's £50 million signing Fernando Torres failed to score, however, and the breakthough came in the 78th minute after the Spaniard had been replaced by Didier Drogba.
The victory extends Chelsea's recent upturn in form and maintains their lingering hopes of retaining the title they won last season - they trail leaders Manchester United by nine points with a game in hand.
More significantly, this win tightened their grip on a top four place, with Carlo Ancelotti's side taking full advantage of fifth-placed Tottenham's failure to beat West Ham on Saturday.
City drop down to fourth and are now the team most likely to be threatened by Spurs.
They paid the price for a lack of adventure in their approach and when Luiz headed home from Drogba's free kick, they had no way of responding before Ramires sealed the victory with a fine run and finish.
Ancelotti's team sheet confirmed the Chelsea manager is still undecided about how to get the best out of his forwards by taking the surprise decision to drop both Drogba and Nicolas Anelka to the bench and pair Salomon Kalou with Torres.
Torres had failed to score for his new club coming into this game and while Ancelotti insists the forward is under no pressure, the player himself admitted in the build-up to this game he was anxious to get off the mark.
City, who were without Carlo Tevez after the Argentina international failed a late fitness test on a groin, started brightly with Yaya Toure forcing an early save from Petr Cech.
But Chelsea soon took control of the midfield with City content to sit back and attempt to catch the home side out on the break.
Florent Malouda, restored to the side as one of five changes to the one that drew 0-0 with FC Copenhagen midweek, worked effectively on the left hand side of midfield.
Yet the quality of service to Kalou and Torres was poor and when Chelsea did manage to create space inside the City area, the chance went begging when Ramires and Kalou got in each other's way.
Torres threatened to break clear just once before the break when he was released by Kalou but was denied by an excellent covering tackle by Nigel de Jong.
Kalou then tested City keeper Joe Hart with a shot on the turn moments before the interval but the home side reached the break knowing they would have to do a lot more to break down City's blanket defences.
While City's attacks were sporadic and lacked conviction, there was no doubt the stalemate suited Roberto Mancini's team more.
Chelsea had stepped up their game superbly to come from behind and beat Manchester United at Stamford Bridge recently and there were early signs they would repeat that performance at the start of the second half.
Malouda linked superbly with Torres and Kalou to carve open the visitors' defence but spoiled the move by firing tamely at Hart in the 51st minute.
Then ten minutes later Branislav Ivanovic was unlucky to see his powerful header deflect to safety off Kompany.
Torres and Malouda were replaced by Drogba and Anelka in the 70th minute and the Ivorian made his impact felt, floating in the free kick for Luiz to head home before Ramires scored a superb solo effort in stoppage time.
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