"His two goals were terrific, the athleticism he showed for the first and the power for the second."
Moyes, who oversaw the start of Rooney's professional career in his previous role as Everton manager, added: "Wayne did well when he came on and made a great run for the one goal and a great pass for the second. He helped the team and played a part getting the result."
Rooney received a standing ovation when he came on to replace club great Ryan Giggs.
"The supporters recognise good players and they recognised that when Wayne came on," said Moyes.
"He's got quite a bad kick down the back of his Achilles and he is still lacking match practice.
"Wayne has worked very hard when he has been fit. You cross that white line and enjoy your football and I thought he did that today."
Although Swansea had dominated much of the game in terms of possession, United struck twice to send Moyes in with a smile at half-time.
Van Persie controlled Giggs's lobbed pass after 34 minutes before beating compatriot Michel Vorm from 10m and then, two minutes later, Welbeck turned in Antonio Valencia's cross.
Van Persie added his second goal - a stunning strike from 18m - after 72 minutes.
Although Swansea striker Bony came off the bench to snatch a consolation, eight minutes from time, Rooney's through ball in stoppage time enabled Welbeck to lob Vorm for his second goal.
"I think like any manager, to win the game there is always an element of relief," Moyes said.
"I thought we were incisive, our finishing was fantastic."
- AAP