Essien hails Luiz impact
Summer signing Luiz broke the deadlock in a cagey affair after 78 minutes when he headed home Didier Drogba's free-kick at the near post.
It was the Brazilian's second goal since moving to West London and was followed by a second from his countryman Ramires to seal a win that moved the Blues ahead of City and into third.
"As you can see he's been fantastic for us since he came here," Essien told Sky Sports. "We need his types of player at Chelsea. He's done a great job for us."
The win keeps Chelsea's faint title aspirations alive. They are now nine points behind leaders Manchester United, with a game in hand.
Essien was, however, coy about his side's chances of retaining their crown.
"We take every game as it comes, we'll work hard in every game and see what happens," he said. "We'll see. We'll have to keep believing that we can do it. There's a long way to go.
"We have to fight for every point, but it was a very important win for us. It was a difficult game for us - we gave everything to get the three points.
"It was a very tight game."