Fernando Torres put aside his early-season travails to strike both goals as the Reds notched a unexpected but impressive 2-0 win over the Premier League leaders at Anfield yesterday.
It was the team's third league win in succession - their fourth in all competitions - and further lifted the gloom which settled over the club last month.
Liverpool slumped into the bottom three as they suffered back-to-back losses to Blackpool and rivals Everton in October - those games either side of an acrimonious takeover battle that ended in the High Court - but the mood has now been transformed.
Kuyt said: "You can see the quality and the strength is coming back into the team.
"Players are starting to get used to each other and the new players are starting to kick on.
"We were just playing better and better. If you beat Chelsea you have the chance to beat everyone.
"It was a great result, it was a great team effort."
Such is the tightness of the table that Liverpool, having leapt from 18th to 12th by winning at Bolton last week, were forced back into 16th by results elsewhere by kick-off yesterday.
Their victory catapulted them back up to ninth - their highest position since after the first game - and they might have gone higher had Maxi Rodriguez taken a late chance.
They are now just two points off fifth place and pressure on manager Roy Hodgson, after a difficult first few months in the job, has started to ease.
Further wins over Wigan and Stoke this week could even put Liverpool, almost inconceivably, back into the title race.
Kuyt said: "Everyone knows when you have a new manager, you have some new players, you might struggle in the beginning.
"That is what we had but we have to forget these things and move on, think about Wigan and try to get three points.
"Winning games is what everyone has to think. When you are Liverpool Football Club you have to win every game, or at least to have a chance win.
"We had a great result. It was tough, some of the guys will be tired, but we will be right up for Wigan. Hopefully we can get another three points."
Kuyt was influential throughout in his first Liverpool game for a month.
The Dutchman showed no ill effects from the ankle injury suffered on international duty as he set up Torres' 11th-minute opener with a superb lofted pass.
The 30-year-old said: "It is hard to come back after four weeks. I just had two sessions with the team and the manager asked me if I was ready. I said yes.
"It was tough but physically I was fine. The only concern was the longer the game was going the more tired the ankle got.
"I had a few knocks on it, sometimes it was a bit sensitive, but I could do everything on it.
"I am really satisfied with the way it went and with the first goal I was happy to help."
Kuyt was also pleased to see Torres hit form after a difficult start to the season.
The Spaniard had struggled since a knee operation late last season and had managed just two goals this term prior to yesterday's double.
"One and one is two - that is what we say in Holland," said Kuyt.
"If the team plays better it will be easier for the one up front.
"To make goals sometimes you need delivery as well, and I thought the delivery was good.
"If the team starts to get more confident they start to get better and the chances will come.
"One thing with Fernando you know for sure - if you give him the chances he will score."
Torres hit his second after good work by Raul Meireles in the last minute of the first half.
Chelsea recovered after the break and Nicolas Anelka hit the bar but Liverpool showed their defensive qualities to hang on for all three points.
Kuyt feels the Reds may now have turned the corner and wants to play a full part as the season goes on.
He said: "It was a really hard time and hopefully it was my last injury this season.
"If you are a football player you want to play every game, especially these kind of games."