Luiz is quickly becoming a Chelsea hero after scoring his second goal since signing in January.
Chelsea leapfrogged Manchester City to third place in Premier League standings after a deserved 2-0 win over their rivals on Sunday.
Chelsea were much livelier at Stamford Bridge with Fernando Torres and Salomon Kalou starting up front. The duo made several good interchanges with French midfielder Florent Malouda, but the City defense stood strong.
Chelsea boss Carlo Ancelotti replaced Torres and Malouda with seasoned Didier Drogba and Nicolas Anelka after 70 minutes, leaving the Spaniard Torres having no chance to celebrate his 27th birthday with a maiden goal for Chelsea.
Drogba, 33, showed his importance eight minutes after stepping onto the pitch as the Ivorian striker crossed a freekick into the box, seeing Brazilian defender David Luiz beat City goalkeeper Joe Hart with a powerful header.
City failed to threaten the hosts although manager Roberto Mancini dispatched forward Mario Balotelli and midfielder Adam Johnson in closing stages while Chelsea pushed further forward with Brazilian midfielder Ramires's individual effort two minutes into stoppage time.
Earlier, Liverpool ended their visit to Sunderland with a 2-0 victory as Dirk Kuyt converted a first-half penalty before Luis Suarez doubled the lead with a tight angle goal in the 77th minute.
Previously on Saturday, Dimitar Berbatov stepped off the bench to score a late goal for Manchester United at Old Trafford on Saturday, securing the English Premier League leaders a 1-0 win over Bolton.
Arsenal fought back from two goals down to draw at West Brom but have been already five points behind the Red Devils.
United were dealt a blow to their already suffering defensive line-up as Wes Brown was forced off at half-time with injury and Jonny Evans facing a suspension after receiving a straight red card in the 75th minute for a foul on Stuart Holden.
The hosts didn't allow themselves to be affected after the dismissal of Evans and finally broke the deadlock in the 88th minute when Berbatov poked home.
Arsenal suffered an early setback when Steven Reid was left unattended to head home after three minutes. The Gunners dominated possession but couldn't grab a leveller before Manuel Almunia conceded a second goal due to his blunder.
In the 58th minute, the Spanish goalkeeper ran out of his goalmouth needlessly and got caught in a mix-up with defender Sebastien Squillaci, only allowing Nigerian Peter Odemwingie to slot the ball into the open net.
The Gunners were shocked but Andrey Arshavin's effort brought them back into the game. The Russian stroked past Scott Carson in the 70th minute after exchanging passes with Marouane Chamakh.
With 12 minutes remaining, Robin van Persie poked the equalizer, but the draw was obviously not enough for Arsenal's title hopes.
