Zola lost no time in fining his former Chelsea colleague after he was arrested this week on suspicion of drink-driving.
But with Dean Ashton out injured and Craig Bellamy not match fit the Hammers manager could not punish Cole further by leaving him out at Craven Cottage.
And the 24-year-old responded with a 43rd-minute opener as the Hammers bounced back from their midweek Carling Cup exit at Watford to move up to fifth in the Barclays Premier League.
He said: "It was the perfect way to respond. He scored a goal and helped the team so much. And because of this I have allowed him to go out tonight.
"Everybody makes mistakes and that is what I told him. As long as you take it in the right way and realise your responsibilities then you realise your mistake. I am pleased with him.
"He had to make up for it. He paid a fine and also had to help the team on the pitch. He is a player that wants to improve and become more important. He is doing great and if he carries on like this he won't only be important for us."
England manager Fabio Capello was in the stands but Zola was not expecting his fellow countryman to add a third Cole to his squad along with Ashley and Joe just yet.
He said: "Carlton Cole is not playing at his best because he needs to improve his finishing. But if he gets that as good as the way he works he could be an unbelievable player."