Goal scorer pays tribute to Toffees 'keeper Tim Howard
The Australian got the Merseysiders off to a dream start at Eastlands as he headed his team in front after just four minutes.
Leighton Baines then doubled Everton’s lead before a Phil Jagielka own goal led to a nervy last 20 minutes for the visitors, especially as they had been reduced to ten men following Victor Anichebe’s sending-off.
However David Moyes’ side were able to hang on for just their second away victory of the season, as City defender Kolo Toure was also sent-off late on.
"The achievement is massive for us," Cahill told Sky Sports.
"We knew we had to work hard but what's been going on in the last couple of months, we've been working, playing some good football and not got the rewards.
"But we've come to a stadium where it is hard to play and showed our mettle and played some good football too."
Everton ‘keeper Howard kept his side in the match with a number of important saves as City desperately looked for an equaliser late on into the game.
Cahill was quick to honour the American shot stopper for his performance, but admitted that he had come to expect such displays from the former Manchester United player.
"He's been the man not just this season but all the other seasons as well. It's what he brings to the team,” he said.
"There's times in games when we look to him to get us out of it and tonight he did that."
Howard himself believed that the three points gained at Eastlands more than made up for having to endure temperatures of minus nine degrees during the match.
"They were on top of us most of the second half and then with the sending off, we knew we had to dig in and fight, we did that to be fair to everyone," he said.
"That was as cold as it gets, but it feels a lot warmer now we've won."