Much had been made during the build-up of a planned fly-by protest, with a plane carrying the message 'Wrong One - Moyes Out' flying over Old Trafford shortly after kick-off.
Things then began badly on the pitch when the home side conceded a free-kick from Ashley Westwood, but Rooney's double plus further goals from Juan Mata - his first for the Red Devils - and Javier Hernandez earned United a much-needed victory to take some of the pressure off the club.
It was the lift Moyes - who was given a rousing reception inside the stadium - and his players needed after the midweek defeat to Manchester City, and Rooney told BT Sport: "Today was a big game for us after midweek.
"We had to respond and it was difficult. We had a slow start, going behind, but we came through it and got the win and deserved it. It was a good win for us.
"We know the support the manager has got from the players and from the fans and that's what matters. The support he got from the fans was incredible again today."
United's attention now turns to the Champions League meeting with Bayern Munich at Old Trafford on Tuesday, a match Rooney is looking forward to.
He said: "It's a massive game, the quarter-finals of the Champions League against the champions. It's going to be a good game and hopefully we'll get a good result."
Moyes was also grateful for the support he received after a week of criticism from many quarters.
"I've been saying all the time since I've been here the crowd have been great, and they've been terrific to me as well," he said.
"Of course at times we haven't done as well as we'd like, and we didn't start the game well today. But the crowd were brilliant the way they got behind the team."
The manager was particularly impressed with Rooney's display and is keen for the England man to keep producing the goals.
Moyes said: "He's a top player. He's been great since the start of the season.
"I said to him after the end of the game 'if you keep scoring two goals for us, it's going to give us a great chance of doing much better'. And his form and the way he's been playing has been very very good."
Moyes now has the task of trying to plot a route past European champions Bayern, a tall order for any manager with the Bundesliga side the in-form club on the continent at present.
But the United boss is relishing the prospect and said: "I'm really looking forward to it.
"We've got a big game, we've got a tough game against probably the best team in Europe at this moment, but bring the challenge on. Coming to Old Trafford isn't an easy place for any team."