The Red Devils made it four wins from four in Group H to qualify for the last 16 of the UEFA Champions League as pool winners.
Rooney netted from the penalty spot after Van Persie had come off the bench to cancel out Alan's opening spot-kick for Braga, while Javier Hernandez scored in stoppage time to wrap up the comeback.
The England striker was full of praise for his team-mates, saying of Van Persie: "He's a fantastic player. He's been a great addition to the team, scoring goals, and he's great to play with.
"Not just him but 'Chicharito' (Hernandez) has been brilliant in recent weeks when he's played, scoring goals, so I think we're sharing the goals out and it's great for the team."
Rooney admits United were not at their best in a game which was delayed for 12 minutes in the second half after a floodlight failure in Braga.
He said: "There's been a few tough games and sometimes we've made hard work of it, to be honest.
"Tonight it was a difficult night and we maybe weren't at our best but we won the game and that's all we can ask.
"Thankfully we're through now and top of the group. We're happy with that."
The striker feels United have added motivation to reach the Champions League final this year with Wembley the setting for May's showdown.
"We're ready and it's a great incentive for us with the final being at Wembley," he said.
"You've seen in previous years, anyone can go on a run and win the tournament. We have to make sure we're at our best and obviously be a bit lucky as well in the draw in the earlier rounds of the knockout stages."