Eden Hazard got his first goal for the club from the penalty spot after Fernando Torres tumbled in the area, and the revitalised Spain striker added the second in first-half stoppage time.
Chelsea have changed their style this summer, but Cole is delighted with how quickly they have gelled.
"We've lost Didier [Drogba], a big powerful presence up front and sometimes we just used to knock it up to him," the England left-back told ESPN. "But now we've signed some smaller players so we've got to get the ball down a play a little bit more now.
"The second goal today was a great goal for the whole team."
It was Torres's third goal of the season, counting his strike in the Community Shield, and Cole reckons the frontman's new-found confidence is as much a result of Spain's triumph at Euro 2012 as his new role in a Drogba-less Chelsea team.
"Of course it was really hard for him to [only] get that many games [last season]," Cole said. "But when he did play he worked really hard for the team.
"Now he's the main man, like you say. But he's full of confidence after the European Championships and he scored a great goal today."
Hazard turned in another fine performance to add to his growing reputation since his big-money move from Lille this summer.
"I think he deserves a lot of credit for the start to the season we've had," Cole said. "He's won two penalties, got two assists and now a goal - it's phenomenal.
"We're proud to have this guy in the team and hopefully he can keep doing it."
Hazard added: "I'm very happy to get my first goal at Stamford Bridge."
The Belgium international opened the scoring from the penalty spot in the 22nd minute before brilliantly laying on the second goal for Torres in first-half stoppage time.
With regular penalty-taker Frank Lampard on the bench, Hazard - who earned spot-kicks for his side in each of their first two games this season - stepped up and directed a low penalty past Tim Krul.
The £32 million (Dh185.8m) winger then back-heeled the ball perfectly into the path of Torres in first-half injury time, who finished coolly into the top corner.