The Old Trafford boss was delighted with his side after it overcame Arsenal and confirmed Nemanja Vidic had traveled to the hospital with a head injury.
The Premier League champions picked up three points after a Van Persie header from a Rooney corner proved enough to overcome the current league leaders.
The Dutchman did not celebrate when he scored against his former club last season, but he did not hold back in Sunday's victory over the Gunners and Moyes has branded his first-choice strike duo "fantastic" following the game.
"Great players score great goals in big games, and Robin's a great player," he told reporters. "His sidekick [Rooney] played great as well. The two of them were fantastic. The big players are coming up when needed and Robin and Wayne gave two big performances."
The win sees United leapfrog Manchester City in the league, while preventing Arsenal from extending its two-point lead, and Moyes is excited by what he thinks was a top victory and what will be a close title race this season.
"It was a big result for us today," he told Sky Sports. "Arsenal have been playing well this season and we had to play well ourselves today to get the result. "I thought we started the game well. I thought we were very good in the opening 30 minutes of the game. I thought our determination, our effort, our commitment and our good play helped us in the second half when we were under pressure."
"Overall it's three important points. I never thought anybody was going to run away with it [the Premier League]. I think there are a lot of ups and downs. It's a close run league this year. I'm pleased we're beginning to show a bit of consistency and a bit of momentum and let's hope we continue that."
Moyes also revealed Nemanja Vidic, who was substituted at halftime with a head injury, was sent to the hospital for scans.
"He has gone to hospital," he said. "It was a terrible clash, it's an accident but hopefully he'll be ok, though I'll find out more from the medics later on."