Chelsea came alive after the interval with two goals in eight minutes, the first a Salomon Kalou header set up by Alex's astute nod across the face of goal.
Chelsea boss Avram Grant admitted he had read the riot act to his players at half time and was pleased with the response.
He said: "I was not happy with the first half. We needed to do what was necessary to win the game because in the first half we didn't play well.
"Most of the time you can speak to the head of the players at half time. The job for a manager is to do the right thing.
"When the players are too nervous the manager needs to be calm, when everyone is too calm the manager should not be calm.
"At half time when you see the players are slipping, you need to wake them.
"Today everything was wrong. We didn't press well or move the ball well. We lost many passes, but we still had two great chances to go ahead and then equalise.
"But I was very happy with the second half. We played good intelligent football.
"The players had more determination and played well. Everything was better at half time."