The match was billed as Tottenham's last real hope of closing the gap to Chelsea, but Everton failed to do them any favours as the pacesetters now sit four points clear despite Spurs' 2-0 victory over Arsenal.
Pedro's stunning 25-yard strike sent them on their way 24 minutes from time at Goodison Park, before Cahill and Willian wrapped things up late on.
And the England international feels Chelsea are almost there, with just four games to go and a far more straightforward run-in than second-placed Tottenham.
"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.
"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 [against Arsenal on Sunday], but we can put our feet up now. It's over to them."