A 3-1 win at Stamford Bridge left defending champions Manchester United 14 points adrift of Arsenal, but moved Chelsea two points behind the Gunners with 16 league games to go.
It was Chelsea's sixth win in seven Premier League matches, at the concession of just three goals, and means Manchester City, Liverpool and United have all lost at Stamford Bridge this season.
"The lads are feeling confident, we're going about our business quietly and we're churning out results at this moment in time so we hope that continues," Cahill said on chelseafc.com.
"There's a good feeling among the squad. We're there, we're in and around.
"Arsenal and Man City aren't dropping points at the moment so we need to be within touching distance. We are, and we're happy with how it's going."
Samuel Eto'o scored all three goals - taking his Premier League tally to six - after justifying Mourinho's selection of the Cameroonian ahead of Fernando Torres.
"I love big games," Eto'o told Chelsea TV. "Before the game I spoke with Jose I told him I like big games and I wanted to play in this game.
"It's tough. He has big strikers, Fernando, Demba. He gave me my opportunity.
"I'm so happy for me, for the team and the supporters."
Eto'o has been linked with a move to Major League Soccer after an indifferent start to his Premier League career, but the former Barcelona and Inter Milan ace would favour a return to Real Mallorca.
He told Spanish radio station COPE: "I have signed all season for Chelsea and I try to enjoy it and then to Mallorca."
Cahill was influential in two of Eto'o's goals, creating the second with an incisive pass before seeing his header saved as the striker scored a third.
"This hat-trick is going to do his confidence the world of good," Cahill said.
"He is a top, top player, a great performer. He's been involved in massive games in the past.
"It's great to have a player of that ability - with all his experience - in our squad."
Chelsea next play Stoke in the FA Cup fourth round on Sunday before resuming Premier League duty at home to West Ham and away to Manchester City.
Torres replaced Eto'o against United, but suffered a knee injury which will keep him out for a number of weeks, meaning Mourinho will give Demba Ba his opportunity.
Ba has not started for Chelsea since the Premier League win at Norwich on October 6 and has been limited to short cameos off the bench when in the matchday squad.
Nevertheless Mourinho insists he has never lost faith in the Senegal striker and repeated that he will not be buying a frontman in the winter transfer window.
"We are not going to make any further investment in this market relating to a striker," Mourinho told Sky Sports News at a Football Writers' Association dinner in London on Sunday night.
"What makes sense is that we always said Demba Ba is not for sale, not to go on loan.
"Demba Ba is important to us, even if he is not playing a lot."
Mourinho's first priority is to secure Champions League football for Chelsea next season, given the club's travails in the last two campaigns.
Chelsea were 25 points adrift in sixth in 2012, but qualified after winning the European Cup, while last season a place in Europe's elite club competition was only assured by a final-day victory over Everton.
The Blues are six points better off than fourth-placed Liverpool after the United win.
"We are trying to create the space between us and the ones outside the top four, because we want to play Champions League, we need to play Champions League," added Mourinho, who believes Manchester City are title favourites.
"We are putting ourselves in a position of that stability. In the last years Chelsea finished outside the top four and last year qualified for the top four in the last match, under big pressure.
"If this season we can be stable and be always safe in the top four, that's very, very important.
"At the same time, if you are safe in the top four, you are not far from the leader and if you are not far from the leader you can enjoy the league in a different way.
"We are not favourites, but we are not far (off)."