The Blues, fifth last term, claimed an eighth win from 11 games with Sunday’s 3-1 victory over Crystal Palace.
The win, secured by Alvaro Morata’s double and a Pedro strike, took Maurizio Sarri’s side into second, above Liverpool on goal difference and trailing holders Manchester City by two points.
“The most important thing is step by step, game by game,” Pedro told Chelsea TV. “The team knows we’re now in a very good position, but it’s too early to know anything.
“There are a lot of games until the end. It’s very important to continue in this moment.”
Eden Hazard returned from a three-game absence with a back problem and performed well.
Pedro added: “He’s the most important player here. He’s a star for us. Eden is playing very good. It’s very good news for us that he’s in very good form.”
Chelsea have never lost in a game in which Pedro has scored, according to the club’s in-house TV channel. The Spain winger said: “This is good, I didn’t know. I’m really happy to score the goal. The team worked very hard.”
The Blues next play Everton on Sunday, after Thursday’s Europa League clash at BATE Borisov in Belarus.
Palace are winless in six league games and next face Tottenham and Manchester United, either side of the international break.
Andros Townsend, who equalised for the visitors early in the second half, rued the concession of a set-piece goal which restored Chelsea’s advantage.
“When you play the top teams the minimum you have to do is not concede from set plays,” Townsend told cpfc.co.uk.
“They are good enough to cut you open, so if you are going to lose then let it be via a great goal from one of their world class players but I’m sure we will learn from that. We will work on it and go again next week and learn from the mistakes we made.”
Palace are on a challenging run of fixtures, after drawing with Arsenal and the defeat at Chelsea.
Townsend added: “It’s difficult, we are playing well enough and creating chances but have been unlucky on one or two occasions.”
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