Hazard's close-range header in the 22nd minute proved enough for Chelsea to follow up Sunday's League Cup final win against Tottenham and maintain their five-point gap over Manchester at the top of the Premier League.
The Belgium international was a constant threat throughout, laying on chances for Diego Costa and Ramires in a superb all-round performance.
"Eden Hazard is fantastic," Mourinho said. "He is punished by opponents in a very hard way.
"Today, not in a violent way, just an aggressive football way because they tried to stop him but the kid is playing, scoring and defending.
"My team were brothers on the pitch and that is important if you are to win the most difficult league in the world."
Chelsea were just about good value for their victory, although West Ham had chances of their own to take a point, most notably Diafra Sakho failing to put a free header past the excellent Thibaut Courtois in the first half.
And Mourinho was delighted to come away with three points that he feels will be crucial in their bid to win the title.
"Courtois was amazing in everything," he added. "A game you can easily lose two points, I am so happy we won.
"The way they [West Ham] play, nobody is better than them. They are the best at the way they play. It is not just to play football - the pressure, the tension and the emotion, my players were fantastic. We couldn't kill the game and these three points are massive for us.
"I told the referee is it very difficult to be a ref here, because of the style of their game - lots of long balls. West Ham had lots of balls in the box. [It was] very difficult, very intense and really difficult for the referee.
"They complain for everything, the crowd is behind them and it is really, really difficult. I want to sleep until midday!"
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