The Stamford Bridge side snapped a four-match winless run in all competitions with the West London derby honours, as Oscar and John Obi Mikel scored after the break.
The result lifted Mourinho's men above early pacesetters Liverpool in the table, and although they are likely to lose that position on Sunday - Arsenal and Tottenham are both in action, while Manchester City face arch-rivals Manchester United - the Portuguese was happy to see his side bounce back from a disappointing seven days, which included defeats to Everton and Basel.
Mourinho told Sky Sports: "Against Everton we went home very, very sad and today we go home very, very happy.
"The result was better than the result against Everton. I still think that we played much better against Everton than we did today but points are also important.
"After a bad start, a start that everybody kept telling me is the worst start for about a decade (for Chelsea)…today I looked at the table, nobody is in front of us.
"The beauty of the Premier League is that everybody loses matches and everybody drops points. The top six teams have already had a defeat, so no dramas.
"I am aware we are not playing very well but we will work, we are top professionals and everybody is working hard."
Mourinho dropped Juan Mata and David Luiz from his squad for the Fulham win, and Oscar – the man favoured by the Portuguese in the playmaker role ahead of Mata – repaid the faith shown in him.
The Brazilian was in the right place at the right time to score in the 52nd minute and Mourinho praised the 22-year-old's versatility, before explaining why Mata had been dropped.
"As a number 10 he (Oscar) gives us creativity and he gives us ability to press up and defend," he added.
"Juan has to learn to play the way I want to play. He has to be more consistent, he has to be more participative when the team lose possession.
"I think it is not his fault, just the way he has played in recent years."
Mikel was delighted after scoring his first Premier League goal in his 185th top-flight appearance but felt the result – the club's first win in a month – was more important.
"We had lost two games in a row and the most important thing to do today was to win. We got the three points and my goal was just a bonus," he said.
"I am pretty happy, it has been a long time. The guys have been killing me about it. It is good to get my first goal in the Premier League, I have scored in the FA Cup a couple of times."
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