Goals from Willian and Diego Costa failed to mask the fact this was Blues first victory since they beat Burnley at the end of August.
Since when, reverses to Liverpool and Arsenal have brought the task facing Antonio Conte into sharp relief.
But as he said, clubs don't get new managers because everything is rosy in the garden.
They get them because they finished 10th with a vast array of talent failing to flourish.
Did he think it still might be better than it is at this stage?
"No, no. It's not a surprise," Conte said.
"Usually, when you change manager, it means you have a problem.
"When you arrive in a place who called you to solve their problems, you know you must face this situation.
"Sometimes you can be happy and solve the situation very quickly. Sometimes you need to have time to solve the situation.
"It's important to understand how many problems you find when you arrive in a new team.
"In my life, my story shows that I haven't ever found an easy situation (when I've come in).”