Mourinho masterminded a significant victory in the Barclays Premier League title race as the Londoners claimed a deserved 1-0 win over previously free-scoring City at the Etihad Stadium.
With City having scored 115 goals in all competitions, it was assumed Mourinho might adopt defensive tactics but he more than matched City at their own game with a fine display of counter-attacking football.
Defender Cahill claims there was never any intention of sitting back and playing solely to cancel out the title favourites.
The England international said: "It makes me laugh when people say that.
"But we were disciplined defensively with the two midfielders and centre-backs staying solid.
"It was a class performance. We had to weather the storm for the first 10 or 15 minutes but the work-rate was fantastic and we managed to get the result we deserved overall.
"Jose has the CV for a reason. He is obviously a top-quality manager and we worked on a few things in the last couple of days which he was adamant we put into practice.
"It did pay off for us and we defended solidly with a fair share of the ball.
"The club is a massive club and when you have that and massive players, and you add a massive manager, I think it combines really well.
"He is experienced and it is all new for me but it is working well at the minute. We are playing well and doing what he asks of us."
Mourinho played down his side's title chances after the game but the Blues are clearly in the reckoning.
Their performance was an excellent response to last week's frustrating goalless draw with West Ham and they will look to maintain the momentum as they host Newcastle on Saturday.
Centre-back Cahill, who was outstanding alongside John Terry on a night of high intensity, said: "I thought every single person put in a shift and played well.
"We know we have quality in the side but we had the desire to chase and break up play numerous times.
"We had loads of possession against West Ham and it was a blow to drop two points at home.
"Now we are on the end of a positive win away from home so we can't afford to throw that away at the weekend against a tough team.
"We are at home, we should be buzzing with confidence and ready to go again."
City made the better start with Yaya Toure and David Silva having early chances but Chelsea then took charge with Ramires testing Joe Hart before Ivanovic fired in a fine left-foot shot from 18 yards.
With Eden Hazard and Willian tormenting the City defence, the visitors could have had more and Samuel Eto'o, Nemanja Matic and Cahill all hit the frame of the goal.
Silva had two late chances as City searched for an equaliser but Chelsea were not to be denied.
They were the first team since Birmingham in November 2010 to prevent City scoring at home.
Cahill, 28, said: "Just before we left the hotel we saw the TV saying they had not failed to score at home since 2010, so hearing that 10 minutes before we set off had us buzzing.
"They have quality players but they also have strength and power and sometimes they steamroller teams. I've seen them out-muscle teams and then their quality comes through.
"We needed to match that from the off and I thought we did. Our creative players were creative and we defended really well and we got a clean sheet, which is rare."
There were numerous stars for Chelsea but the performance of £21million Matic, who arrived from Benfica last month as Juan Mata left for Manchester United, did earn praise.
Cahill said: "When you are winning people don't tend to say too much.
"A fantastic world-class player has left the club, no doubt about it, but we have added another great player and he has started two matches and been fantastic in both of them."
- Sports & Recreation
- Branislav Ivanovic