The visiting Blues dominated the encounter at Old Trafford from the start and created the first chance with four minutes on the clock. Nikica Jelavic raced clear of the United defence but his shot was held by David de Gea.
Up the other end, United winger Nani sent two efforts from distance straight into the palms of Everton goalkeeper Tim Howard.
Having controlled large parts of the half, the away side broke the deadlock in the 33rd minute. Tony Hibbert sent over a deep cross which Jelavic managed to loop over De Gea and into the corner of the net.
Champions elect United responded positively and drew themselves level four minutes before the whistle. Nani crossed from the left for Rooney, who guided a header past Howard to score his first goal in six outings against his former club.
If United claim the victory, they will open up an eight-point lead at the top of the Premier League table.