The Blues moved above Liverpool and Manchester City with Sunday's 1-0 win at Middlesbrough - their sixth straight victory in the competition.
However, Luiz knows Antonio Conte's men cannot ease up if they are to achieve their dreams for the season.
The Brazil international told Chelsea TV: "It's important to finish at the top of the league
Of course we are happy, but it's too early to speak about that.
"It's important in the last game to finish at the top of the league
That's our goal."
Diego Costa's lone strike was enough to settle affairs at the Riverside Stadium as promoted Boro made life difficult for the visitors and the result remained in doubt until the death.
However, the miserly defence which has provided the foundation for Chelsea's recent push held firm once again to record a sixth successive clean sheet in the league.
They have not conceded a Premier League goal since Mesut Ozil put Arsenal 3-0 up at the Emirates Stadium on September 24, a run of 590 minutes.
Luiz said: "We are happy
We are doing an amazing job, but we need to keep our feet on the floor with humility because every game is a tough game.
"It's a tough game when you play here (Middlesbrough), everyone knows, so we are happy because we did a great job, especially on the defensive side.
"It's a good three points and the first time this season we are top of the league
But we need to understand it's just the beginning."
Luiz has prospered since his Â£34million summer return to Stamford Bridge from Paris St Germain, lining up in the middle of a three-man defence.
Asked about his new role, he said: "I just try to do my best, it doesn't matter which position I play
I think everybody understood about this philosophy - that's why we are doing well.
"The spirit is amazing and when you have this team spirit, this makes the difference
I am happy to play for this team and I am happy to be part of this family."
Chelsea's title credentials will be put to the test in their next two fixtures, first hosting Tottenham on Saturday before a visit to Manchester City a week later
Source : PA