Rooney's new deal with the Red Devils is reported to be worth £300,000 per week and will keep him at the club until June 2019.
The 28-year-old frontman had previously appeared keen to leave the reigning Premier League champions, with Chelsea having two bids rejected during the summer, but Evra says his team-mate fully deserves his new contract.
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Rooney celebrated his new deal with a superb goal against Crystal Palace as United ran out 2-0 winners, and Evra, who provided the assist for Rooney's strike, was impressed with his finish.
“What a great finish it was, my cross was not easy to take, but it was a great volley," he added.
“It was job done. It was really important, we have had some bad results and tonight 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."
The game also saw Nemanja Vidic and Rio Ferdinand feature at centre-back and Evra says the duo can give Manchester United a boost defensively.
"It's good to have them back, they looked really strong tonight. We had a lot of experience, and, when Rio came on at Arsenal, I thought he was fantastic,” he said.
“You could see tonight with Rio and Vida in good form that we can be solid and get more clean sheets.
“But 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's important for the team.
"I'm happy to help the team, but most important was the team performance. It does not matter if I'm Man of the Match. I'm just happy with the three points because what matters to me is Man United winning, not Patrice Evra winning Man of the Match.”