Morata became the first opposition player to score at Atletico’s new Wanda Metropolitano stadium.
Chelsea went in at the break 1-0 down after Antoine Griezmann scored from the spot five minutes before half-time.
But Morata continued his scintillating form in front of goal by grabbing the equaliser for the Blues just before the hour mark.
Antonio Conte would have no doubt been happy with a draw away at a side like Atletico but Michy Batshuayi ensured Chelsea would return home with all three points with a goal in the dying seconds of the game.
Morata’s equaliser came courtesy of a cross from Hazard and the Spain international lavished praised in the tricky winger.
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“It’s easy to play with a player like Eden,” Morata said.
“He’s one of the best players int he world and I’m very lucky to play with Eden.”
Chelsea now sit top of their group with Roma two points behind and Atletico five adrift.
Morata knew the importance of getting a positive result against the La Liga side but insists their attention will now switch to the Premier League match against Manchester City this Saturday.
“It is a very important win for us. It was a big test,” Morata said.
“Atletico Madrid were in the Champions League final a few years ago and now we can go home relaxed and put this mentality into the Premier League.
“We take the three points and now we can go home, relax and put the mentality into the Premier League but it’s a massive victory today.
“I’m happy but the most important thing is the win. Win the three points and score when possible.”