Robin van Persie and Danny Welbeck both netted a brace to get Moyes’s reign off to the perfect start.
However, it was noticeable Rooney did not join in the touchline celebrations for Van Persie’s second, whilst he was nursing an injury as Welbeck took the acclaim for his delicate injury-time effort.
But Moyes claimed there were no problems regarding Rooney’s dedication, saying: “When you cross that white line it is very difficult not to be committed.
“Lots of people are judging you.
“When you cross that white line it is up to you. I thought he was incredibly committed for the team and helped set up two goals.”
After missing all United’s pre-season games amid talk he wants out of Old Trafford, Rooney got an hour under his belt for England against Scotland on Wednesday.
He added an additional 30 minutes to that yesterday after replacing Ryan Giggs and Moyes was satisfied with the 27-year-old’s contribution.
“Wayne did well when he came on,” said Moyes. “He made a great run which opened up the chance for Robin to move the ball on to his left foot for his goal and the ball he slipped through for Danny was well weighted. He helped the team today in getting the result.”
United’s supporters also backed the forward, chanting his name both as he warmed up and on his arrival into the fray.
“The supporters recognise good players,” said Moyes. “They do that at Manchester United. They recognised that when Wayne came on.
“He is a good player and he showed that with some of the actions he did in the game.”
But Rooney did pick up a knock, although he does have nine days to recover before United’s blockbuster showdown with Jose Mourinho’s Chelsea on 26 August.
“He got a kick,” said Moyes. “It was quite a bad one down the back of his Achilles. He is still lacking match practice but I gave him another 30 minutes today and that will bring him on.”
Moyes was equally happy with the contribution of his goalscoring forwards.
As a back-to-back Golden Boot winner, Van Persie already has four for the season following his double in the Community Shield win over Wigan.
Welbeck, meanwhile, has doubled his meagre league tally from last season, with Moyes particularly impressed by the tap-in from Antonio Valencia’s cross for his first. “I think Danny’s goal against Scotland might have helped lift his confidence,” said Moyes.
“If you are going to be a centre forward you need to get tap ins. He was in the right spot to score.
“Robin has been a pleasure to work with. I have really enjoyed seeing him in action. You might think how good can he get? But he is someone who wants to keep working to get better and find new ways of scoring goals.”
Moyes confirmed he still hopes to add to his squad before the transfer window closes but that: “I couldn’t say, yes, there is something on the horizon.”
For Swansea boss Michael Laudrup it was a chastening experience, with the only consolation being a goal on his debut for record signing Wilfried Bony.
“Our plan was to put Manchester United under pressure,” said Laudrup. “It succeeded quite well until the 33rd minute. Van Persie didn’t touch so many things and suddenly you saw the difference.
“Once a team like Manchester United gets more confidence they can play the ball around like that.”