In a first 45 minutes dominated by an in-form United side, it was Everton that started the brightest with both forwards having half-chances in the first ten minutes.
Former Reds hit-man Louis Saha created a shooting opportunity for himself on the edge of the box but a last-minute lunging block by Nemanja Vidic ensured his keeper did not have to make a save.
Moments later Yakubu couldn't find the touch he needed to turn a teasing cross home.
United started to find their feet and put pressure on the Toffees back line with attempts from Cristiano Ronaldo and Fletcher but the Blues defence stood firm.
Visiting captain Ryan Giggs looked to be in a different class to the rest of the field in the middle of the park as he seemed to have all the time in the world to pick out passes and create the majority of chances.
Camped on their own 18-yard box, Everton struggled to find any outlet as wave after wave of attacks kept coming and Fergie's men took the lead on 22 minutes after Giggs was given time to turn by Steven Pienaar.
The Wales international split the Blues back line to find the onrushing Fletcher who side-footed the ball through Tim Howard's legs to give his side a deserved lead.
Former United keeper Howard had to be on the top of his game to keep his side only one goal behind and the shot-stopper pulled off the save of the match on 26 minutes when he pushed a stinging 25-yard shot from Ronaldo out for a corner.
Howard was called into action again from Giggs' inswinging corner when Dimitar Berbatov's header brought the best out of the American keeper.
Berbatov should have doubled his side's lead just after the half-hour mark when a perfectly weighted pass from Wayne Rooney released the striker but, opting for a chip instead of power, the striker guided the ball into a grateful Howard's arms from eight yards out.
Looking for his 100th career goal, Rooney found himself inside Everton's six-yard box, just before the break thanks to a pin-point cross from Ji-Sung Park.
However, the in-form England man didn't have time for a shot before a well-timed challenge from Phil Jagielka cleared any danger.
Lucky to be just one goal behind at the break the home side re-emerged for the second half a better and more determined team as they chased everything down.
Saha had the first chance of the half with a turn and shot from the edge of the box but again his effort was blocked by Vidic.
Mikel Arteta started to get more of the ball and the Spaniard found the space to send in a low cross that sat up nicely for Fellaini who couldn't get his shot on target.
Challenges started flying in from both sides and tempers flared after a tackle from Everton captain Phil Neville left him with a yellow card and Ronaldo rolling around the pitch in apparent agony. However, replays showed Neville's tackle was perfectly timed.
Everton kept the pressure on United who looked very uneasy at the back and it was a Neville cross that provided the platform for the Blues to draw level.
Neville's 63rd-minute lofted cross to the near post found the towering Fellaini who out-jumped Vidic to nod home his first goal at Goodison Park.
Lifted by the goal the home side went all out for the win and could have taken the lead two minutes later after a lack-lustre back-pass from Rio Ferdinand handed Yakubu a striking opportunity inside the box. However, a well-placed van der Sar managed to tip his shot onto the post.
The biggest talking point of the game came with 20 minutes left when a late challenge from Rooney on Arteta resulted in the former Everton hero being handed a yellow card which triggered a chorus of boos from the home crowd.
Clearly upset by the chants the striker angered his once loyal supporters by kissing his United badge and signalling to the traveling fans. Ferguson reacted by swiftly hauling off his star striker and replacing him with Nani.
Either side could have won the game in the final ten minutes with efforts from Nani and Yakubu both being blocked by some last-ditch defending.
The final chance fell to Ronaldo who found himself unmarked inside the box but the tricky winger pulled his shot well wide.