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."