United struggled to break down a stubborn defense throughout the first half but Rooney scored in the first minute of the second period with a low shot into the bottom corner from Nani's pass.
Rooney added his second in the 84th with a first-time shot into the far corner from Dimitar Berbatov's cross and then helped set up his fellow striker for a headed goal with a minute left.
United manager Alex Ferguson said Rooney could top the 42 goals scored by Cristiano Ronaldo two years ago.
"I said a while ago it's impossible for a player to get 42 but he is on 32 and there is a challenge there for him," Ferguson said. "He has 13 possible games and you never know. I wouldn't put it beyond him.
"I was just glad he got to the 30 mark, but we are enjoying his goal scoring." Rooney's 31st and 32nd goals of the season helped take United to 66 points, two clear of Chelsea and Arsenal.
Chelsea beat West Ham 4-1 on Saturday and has played a game fewer than its title rivals, who each have just eight matches left.
"You have to think about goal difference," Ferguson said. "We are only four goals ahead of Chelsea. I wish it was 14 to be honest, but at least it is in our advantage." Manchester City missed the chance to go level on points with fourth-place Tottenham with a 1-1 draw at Sunderland.
Sunderland led through a ninth-minute goal from Kenwyne Jones, who was left unmarked to head in a cross by Steed Malbranque, but substitute Adam Johnson curled in a late equalizer from the corner of the area.
Although City narrowly avoided defeat, it has won one of its past six matches and is two points outside the Champions League qualifying places.
United had most of the pressure and possession in the opening half at Old Trafford but Fulham had chances from a shot by Clint Dempsey that flew just over the bar and one from Zoltan Gera that went wide.
Dempsey started for the first time since injuring his right knee Jan. 17. He returned as a 61st-minute substitute in Thursday's 3-1 Europa League defeat at Juventus.
Fulham goalkeeper Mark Schwarzer did not have to make a save until the 30th minute, diving full stretch to keep out a first-time shot from Rooney.
United dominated after the break, with Rooney sparking the move that led to his 15th goal in 12 matches. He passed out to Nani on the left and hit the return pass past Schwarzer.
Bobby Zamora had a chance to equalize with 15 minutes left when he got past Nemanja Vidic and raced in on goal. But the United defender recovered to block his shot with a perfectly timed sliding tackle just inside the area.
United then went close with a header by Berbatov, a shot by Patrice Evra and a shot by Darren Fletcher that Schwarzer saved one-handed.
Rooney doubled United's advantage by playing a pass out to Berbatov on the right and shooting from near the penalty spot from the return pass.
He then played a key role in United's third goal, hitting a pass wide right to Park Ji-sung, who curled in a cross that Berbatov headed at the near post for his 10th goal of the season.
