The 28-year-old was the centre of attention going into the game having penned a new £300,000-a-week deal and he thrashed home a magnificent second goal to add to Robin van Persie's penalty and secure a 2-0 win for David Moyes' side.
With Rooney's future in doubt going into the season he has now committed himself to United and wants to continue pushing the champions towards the Barclays Premier League top four.
"I've been trying to do well for the team and trying to help us win," he told Sky Sports 1.
"Whether I'm signing a new deal or not I always give 110 per cent on the pitch and that's what I've done today.
"Obviously I've been letting my football do the talking but I'm happy and settled."
Palace kept their visitors honest in the opening 45 minutes but, after a spell in the ascendancy, conceded a penalty just after the hour as Marouane Chamakh fouled Patrice Evra just inside the area.
Van Persie stepped up to put United in front before Rooney added his fantastic second six minutes later and the England international was pleased with the manner of the win.
"It was a good victory," he added.
"I thought we played well and it was a good win. We moved the ball well, maybe could have created more chances but overall we were in control of the game and once we got one goal we knew we'd get another and see the game out.
"It's tough getting that first goal but thankfully Robin put the penalty away and I think it was a great three points."
Moyes also praised the work-rate of Rooney, whose new contract will be good news for the United boss following a first campaign that has never really taken off.
"Sometimes when Wayne has not got time to think, he does things naturally," said Moyes.
"He has natural talent and the technique and ability to get his weight behind the ball and strike it cleanly was good.
"He works really hard for the team and some of his passing was fantastic. His finish was great.
"He is a really important player and you think about the amount of clubs who wanted to sign him.
"He would have been too difficult to replace. There aren't enough top players out there that you can get cheaply or easily.
"Wayne's one of them, one of the top players. He shows it week in, week out for us and you can see the change in him - his leadership, what he's trying to bring to the team."
Moyes will now take the Red Devils to face Olympiacos on Tuesday for the opening leg of their Champions League tie, with the former Everton manager looking to string together some positive results following their win in south London.
"We have a really big European tie coming up on Tuesday night and our focus goes onto that," he said.
"We wanted to win the game to make sure we go into that game in good form and confidence. It's such a big game for us.
"We haven't played for ten days so I wanted to make sure all the players were ready and focused for the game and ready to perform again."
Tony Pulis saw his side slip to only their second home defeat since he replaced Ian Holloway at Selhurst Park in November but the Welshman still acknowledges his side are in the fight for a survival.
"Every game whether it's home or away matters," he said.
"We have to start collecting the points. We're in it with 12 other teams. It will go right to the end. Whether it's against the top four or five, there's always three points. We have to scrap and fight for everything against every team.
"Today was disappointing. That [the penalty] gave United the leg up they were looking for."