Louis van Gaal's men headed into the fixture knowing victory would lift them to the summit following City's 4-1 loss at Tottenham Hotspur.
That scenario doubtless added to the frustration of the home supporters as United failed to craft a meaningful opportunity for much of the opening half.
Yet they still headed into the break ahead after Depay finished a fine move for his first league goal since joining United from PSV Eindhoven in the close season.
Rooney's long-awaited goal came just after the break and Mata added a third late on to cap another miserable afternoon for the Wearsiders.
A hamstring complaint meant Jermain Defoe had to settle for a place on the Sunderland bench, with Fabio Borini leading the line.
The Italian had little opportunity to make an impact during the early exchanges, however, as United enjoyed the lion’s share of the ball.
Yet their possession was not yielding chances, and Sunderland threatened first when John O'Shea's looping header forced a simple save from David de Gea.
De Gea required a better stop midway through the opening half, the Spaniard using his legs to keep out Jeremain Lens' fizzing half-volley.
The hosts quickly settled back into a composed passing rhythm, although their final ball was leaving a lot to be desired.
United's first real moment of quality brought an opener in first-half injury time.
Daley Blind's superb diagonal ball found Mata's clever run, with the Spaniard playing a controlled first-time pass for Memphis to slot into an empty net.
A second came instantly after the restart as Rooney ended his recent dire run.
Anthony Martial brilliantly worked his way past Younes Kaboul before firing in a cross that hit the skipper's knee and flew into the net.
Sunderland responded impressively and almost reduced the arrears when Ola Toivonen was denied by De Gea.
De Gea had to be on high alert again soon after as Patrick van Aanholt raced on to Borini's delicious through-ball - only to hit straight at the goalkeeper.
But his poor finish paled in comparison to Memphis's in the 67th minute, the Dutchman somehow failing to beat Costel Pantilimon when clean through after some superb work from the impressive Martial.
United did make it 3-0 in the final minute though as substitute Ashley Young crossed from the left for Mata to fire high into the net.
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