After Graham Cummins gave the visitors a 38th-minute lead, Evans equalised four minutes later and struck the winner in the 83rd minute.
Evans also had a weak penalty saved in the 31st minute after he was fouled by Aaron Brown.
Wilson said: "It was a fantastic three points for us. Missing a goal, going a goal down and then winning the game was a fantastic effort from the lads.
"It was a physical game but I think there were pockets when we played well. It's not always going to be fluid football and sometimes you've got to battle and roll your sleeves up.
"We always thought this would be a very tricky game but the composure and calmness we showed at times was terrific. We have to keep looking above us because Charlton are still doing very well."