Rooney signed a £300,000-a-week deal on Friday and, with all eyes on him at Selhurst Park, he struck a superb sealing goal in a 2-0 victory after Robin van Persie had opened the scoring from the penalty spot.
It was the England international's first goal since Boxing Day as he celebrated his new contract in style, with Evra revealing he is pleased to have Rooney tied down.
"He deserved to have a big contract," Evra said.
"I'm so happy for him because he is working hard, and it is a good sign for the future of Manchester United, for the fans and for everyone.
"I'm really pleased with 'Wazza' because he deserves it. What a great finish it was, my cross was not easy to take, but it was a great volley."
United moved ahead of Everton into sixth place in the Premier League with the hard-fought win with Evra glad to end a recent poor run.
"It was job done," he said.
"It was really important, we have had some bad results and we could not afford another defeat. I think we saw a strong Manchester United, confident to play with the ball, and I'm really pleased for all the lads."
Following on from a goalless draw at Arsenal 10 days earlier, the shut-out at Selhurst Park was the first time United have kept two successive Premier League clean sheets under David Moyes.
"We had a lot of experience, and when Rio came on at Arsenal, I thought he was fantastic," he added.
"You could see with Rio and Vidic in good form that we can be solid and get more clean sheets.
"Don't forget Chris Smalling can play there, Phil Jones and Jonny Evans can get back from injury. We have good centre-backs and that is important for the team."
The defeat for Palace was only the second time they have lost at home since Tony Pulis replaced Ian Holloway in November.
A good run of results has seen the Eagles move out of the relegation zone, although Pulis' side are only two points clear of the bottom three.
Midfielder Mile Jedinak was left despondent by the defeat with Palace having been on the front foot before Marouane Chamakh felled Evra inside the area on 62 minutes.
"We had them under a little bit of pressure before that first goal so we'll take a lot of positives from that," he said.
"We've just got to keep building. The word 'disappointment' comes to mind, but it was encouraging nonetheless.
"It was a defeat, but we let them off the hook a bit. We gave them a penalty through a challenge which was probably a rash decision at the time. Those things can happen in football."
Palace travel to Swansea next Sunday as they look to move further clear of the drop-zone and Jedinak is keen to move on from the United defeat.
"Our next game is on Sunday against Swansea away so we've got to regroup, regather, put this out of our system and keep building," he added.
"There is not time to feel sorry for yourself. We will pick each other up, dust it off and get right back to work."