Ji-sung Park's first half header took Sir Alex's men two points clear at the top of the table and the Reds also have a game in hand over the three teams behind them - Arsenal, Manchester City and Chelsea.
Evra hailed United's team spirit after the victory over the Gunners and is now looking forward to next Sunday's clash with Chelsea at Stamford Bridge.
"This is a great win for us, but now we have a big game against Chelsea. If we can play with the spirit we showed tonight, I think we can win many games," the Frenchman told Sky Sports.
"We showed we are a powerful team. Arsenal are a good side and they put pressure on us when we missed the chance to get a second goal. But we stayed strong and everyone defended together.
"We're very happy with the result - we were all very focused and determined to work hard and that's why we got the win we deserved."