The England striker opened his account with a free kick on Saturday.
David Moyes has challenged a reinvigorated Wayne Rooney to hit 30 goals for Manchester United this season.
Rooney was continually linked with a move away to Chelsea during the summer transfer window amid speculation that he wanted to leave Old Trafford, but eventually decided to remain with the Premier League champions.
The 27-year-old was reportedly unhappy at being asked to play in midfield and out wide by Sir Alex Ferguson last term after being usurped in his favoured role up front by Robin Van Persie.
However, Moyes hinted that Rooney will be restored to the United attack alongside the Dutchman and confirmed that he would be setting him a goal target.
“I will try to do that,” he told Metro. “I think Wayne’s aim will be to do that as well. Hopefully we can make that happen.
“The hope is that we get a partnership where folk are saying, ‘My goodness we are having to play against Robin van Persie and Wayne Rooney’.
“Everybody is looking to see if those two form a partnership that can score lots of goals.”
Rooney scored his first goal of the campaign with a free kick in the 2-0 win over Crystal Palace on Saturday.