The English Premier League side, who face Mexico's Monterrey in their semi-final in Yokohama on Thursday, took four games to register their first win under the Spaniard.
However, nine goals in their last two matches have given Chelsea a boost for a tournament they are under pressure to win after an embarrassing group-stage exit from the Champions League.
"Since [Benitez] came we have tightened up as a unit defensively and as a team," Cahill told reporters.
"That's given us a platform to build on. It was hard at first to get his points across because we were playing games almost every other day.
"Now the players are adapting, they know what's expected of them and it's working well at the minute."
Cahill said the Chelsea players had realised the significance of the Club World Cup since flying out to Japan following Saturday's 3-1 win at Sunderland.
"Since coming here it's sunk in now how big it is," the centre-back said. "It's hard to get into the competition in the first place.
"We've come all this way and want to win it. Our Brazilian players have said it's absolutely huge for them and we saw the send-off [Corinthians] got at the airport."
Some 15,000 Corinthians fans saw off their team in Sao Paulo, waving banners and letting off fire extinguishers in the airport lobby.
DREAM CHANCE
Chelsea have Brazilians David Luiz, Ramires and Oscar among their ranks and Benitez echoed Cahill's sentiments about how much the Club World Cup meant to them.
"They said it was a dream for them to play in the tournament," said Benitez, who won the trophy with Inter Milan in 2010 and was a runner-up with Liverpool in 2005.
"I intend to win the tournament," said Benitez, who replaced the sacked Roberto Di Matteo last month.
"I will use the best team possible - you can't leave it for the final. You have to win your semi-final."
While club captain John Terry remained in London for treatment on a knee injury, Frank Lampard is likely to play a part after overcoming a nagging calf problem.
"Frank Lampard will be available," confirmed Benitez, who knows any slip-ups in Japan could prompt trigger-happy Chelsea owner Roman Abramovich to hire a new coach.
"My main focus is to get the players to sleep for more than four hours.
"My experience with this tournament is to look at the condition of the players in training. Some are fresher than others. We have plenty of options."
With Fernando Torres rediscovering his touch after an alarming drought and scoring four goals in the last two games, Benitez even cracked a joke about Abramovich.
Asked if he had received any message from the Russian tycoon, Benitez said: "Not at the moment. But I'm not planning on playing Abramovich at centre-forward; I prefer Torres."
