Eden Hazard and Fernando Torres, on his 200th Premier League appearance, were the scorers as the Blues moved above Arsenal and Manchester City for 24 hours at least.
Jose Mourinho's men have now won four on the trot in the league and Cech is eager to keep that run going.
"The most important thing is that we keep winning games and winning trophies," he told BT Sport.
"We want to win the league if we can and hopefully clean sheets will help us achieve our targets. Now we're top of the league for the first time in a long time and hopefully we can stay there.
"We hope to keep going. We are getting better and today was a very difficult game. But we were very solid and good in attack and that's why we score goals.
"We are a young team and hopefully we can take advantage of that."
There has been some speculation over Hazard's future in recent days, with Mourinho stating the Belgian international would not be leaving the club despite reported interest from Paris St Germain.
And the Chelsea boss reiterated that stance on Saturday, although he is keen not to put too much expectation on Hazard's shoulders.
"The club made that decision because every manager wants a player like him," said the Portuguese coach.
"I'm not expecting to put too much pressure on him or for him to be the man of the match every game, but what I expect from him is his motivation, his commitment, his responsibility.
"This season I think you are watching a much more mature player and because of that he is becoming a fantastic player."
Having failed to find the target against Chelsea, Hull counterpart Steve Bruce is hoping to strengthen his attacking line this month, having agreed a fee with Everton for Nikica Jelavic on Friday and also been linked with another move for West Brom's Shane Long.
He said: "A new player always brings a little bit to the squad, a bit of impetus. Let's hope we can get both. You're never sure how it can go but we're trying our best."