The Brazilian headed home the third goal having already seen one strike ruled out for offside, as United took a 3-1 lead in the game in the first half.
And having seen new arrivals Robin van Persie and Shinji Kagawa get on the scoresheet, the 22-year-old is predicting a high-scoring season for the club.
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"Everyone knows everyone has these skills and everyone scores," Rafael told MUTV. "We will score a lot of goals this season, I hope.
"I know I've not scored many goals, but I'm very happy. I hope to score more goals. I enjoy my game, I'm just getting mature now and I love football, so it's all good.
"You can see Van Persie is just a top goalscorer. All the time he has a chance, he can put the ball there. What a goal. He's a top player and I'm very proud for him. [Kagawa] is a quick player. He has abilitly, skills... I think he has a future here in Manchester!"
However, it was not all plain sailing at Old Trafford, with the hosts enduring some nervy moments as Fulham went in search of an equaliser, and Rafael accepts that there are concerns about the defence, but says that the return of Jonny Evans will make a difference.
He added: "We let them score the second goal and it was hard when this happened. They were motivated by the goal but in the end it was a good result. Jonny Evans is back now, so that's good for us."