Didier Drogba insisted that Chelsea had to beat Liverpool to banish the memories of their 3-1 defeat by Wigan last week.
The Ivory Coast international made both second half goals for Nicolas Anelka and Florent Malouda and added that it was important to beat a title rival.
Drogba said: "We were disappointed with what happened at Wigan, so we had to win this game. That's what we did."
Chelsea dominated the game to inflict a third defeat of the season on Rafael Benitez's side.
The Reds failed to test stand-in goalkeeper Hilario, playing in place of the suspended Petr Cech, and Fernando Torres and Steven Gerrard failed to shine.
Hilario believes it was an important victory as they failed to land the title in the last few seasons because the Blues dropped so many home points at Stamford Bridge.
"It's important to be top," said Hilario. "In the last couple of seasons we've dropped points at home and lost the title because of that, so this was important.
"There's always pressure coming into big games like this, but I'm not afraid of that pressure. It's a kind of pressure I like."
Meanwhile, Benitez insists his side can still mount a title challenge despite losing their third game of the season. It is more than 40 years since any team has gone on to win the top flight crown after losing three of their first eight games. But Benitez is unconcerned by the statistics.
"I feel the performance wasn't bad against a good team," said Benitez. "We worked hard, had some good play. Defensively we were good enough. They didn't have too many chances, so we were defending better. We didn't have too many chances, which means they're also a good team."