Robin van Persie gave the Red Devils a 45th-minute lead from the penalty spot after Ashley Young, who had already been booked for diving, was adjudged to have been fouled in the Palace area and Kagisho Dikgacoi was sent off.
United produced a dogged and at times uninspiring performance and Rooney, starting his first Premier League game of the season, secured three points with a 81st-minute free-kick.
“He [Rooney] tired a bit in the second half but I thought he was great,” Moyes told BT Sport.
“But we wanted to give him 90 minutes. It’s important we give him as much match practice as we can. We’ve got a big week coming up.”
On United’s overall display, Moyes added: “I think it’s been similar to how we played recent games.
“We needed to score a few more goals when the opportunities arose. Our build-up play and style of play was very good. I was pleased.
“When it was 11 v 11, we played very well. We gave them one opportunity in the game. So we played really well today.
“We couldn’t quite get the goal [in the early stages] but I was delighted when we got it. It was even better when we got the second.”
ENHANCED ODDS: Get 10/1 on England to beat Italy