A stunning strike from Pedro along with further goals from Cahill and substitute Willian helped Chelsea overcome a stubborn Everton side to go temporarily seven points clear of second-placed Tottenham.
With Spurs having a tough game on their hands in the form of the north London derby against Arsenal at White Hart Lane, Cahill admitted beating Everton was like winning a Cup trophy because of the pressure it would have piled on Mauricio Pochettino's in-form side, who have won their last eight straight league games.
"We get a result, it feels massive, then they [Tottenham] respond," Cahill told Sky Sports.
"It's been like that every week. You can see from the celebrations, this was like a cup final for us, one of our hardest with the form Everton have been in at home. To win 3-0 is fantastic.
"It was convincing but we had to work hard for it. Pedro's goal was special, at times you need a bit of class to open up a team, that's what he did today. I'm buzzing with that, it's a huge result for us."
He added: "We have been saying we expect Spurs to win every game and it's down to us because winning the title is in our hands.
"It's got be disheartening for them to have won eight or nine games on the spin, and to keep having to do it. But credit to them, they are pushing us to the end.
"They have got a huge game this afternoon but we can put our feet up now. It's over to them."