After a typically whole-hearted display, Rooney was substituted on 82 minutes and could only watch as Everton capitulated in a frantic closing period.
Rooney returns to Old Trafford where he scored plenty of goals for United but how will he be received now that he comes as an opponent.
United moved level with rivals Manchester City at the summit - the two teams' records being identical after five games - by producing a late flurry to push the Toffees aside at Old Trafford on Sunday. Maybe I give them also one year, one season to adapt.
Both clubs are locked together on 13 points from five games, with 16 goals scored and two conceded each, with City only ahead of United on alphabetical order.More news: Modi, Abe to set 'future direction' of partnership this week: MEA
United responded and nearly went 2-0 up on 65 minutes but Juan Mata's well taken free-kick from the edge of Everton's box came off the post.
However, despite the scoreline, Koeman insisted he felt there were signs of improvements and the result could have been much different if either Wayne Rooney or Gylfi Sigurdsson took the chances that came their way.
"It does not matter if you win on 1-0, 3-0, 4-0, or 2-1, as long as we win".
But Mourinho is certain that this is just a blip for Koeman and Everton. "For me, the second goal was the most important not the third, but it's always nice for him, it's one more goal and strikers always like to score goals".
There has been speculation that Jose Mourinho is angry with Herrera for inviting an inappropriate friend to the training ground at the end of last season, but the Manchester Evening News claim there is no truth in those rumours.