The Spain international completed a £37.1 million move from rivals Chelsea on Sunday, and put in an assured performance in the reigning champions' 2-0 victory over Cardiff City at Old Trafford on Tuesday.
Manager Moyes was also boosted by Van Persie's return from a thigh injury that has ruled him out since December, with the Dutchman opening the scoring with a close-range header.
Ashley Young added the second with a superb solo effort, and Moyes was able to introduce Rooney for the final half-an-hour after he missed the last five games with a groin issue.
The Scot was thrilled to have the trio at his disposal, and feels the side will improve their current position of seventh with them in the team.
"It was good to get a team with Robin back on the pitch, give Juan his debut and great to get Wayne back on the bench and give him some minutes at the end," Moyes said.
"I thought Juan did really well, created some good chances for us. I was concerned about his match fitness but we got the second goal and I was able to give him some more minutes and keep him playing.
"It was the same with Robin - we knew we could only give him 60 minutes, and (the same with) Wayne who only started training on Monday.
"The results with them will get much better, we need to get them into the right physical condition. They need match practice and match fitness. I was really pleased with them."
Mata was employed behind Van Persie who started as the lone striker, but Moyes concedes he will look to utilise his versatility going forward to accommodate all three players in his starting XI.
He added: "I can play him off the left, off the right. I can keep Robin and Wayne as a partnership, I'm comfortable with that. Anytime I need him (Mata) to play a different role, like number 10, he can do that."
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