Against the run of play, Zaha broke through on 38 minutes, picking up the ball 40 metres out and jinking through two defenders before firing an unstoppable shot past the keeper.
Huddersfield were unlucky not to take at least a point, with Aaron Mooy hitting the post, but have struggled in front of goal this season and have now gone five home games without a goal -- their worst run since going six in 1972.
Zaha denied Palace were too reliant on him, saying: "We are a team. Without them I wouldn't be able to do what I do. If I manage to score for them, I do for the team."
The goal was his eighth in 10 Premier League games -- as many as he scored in his previous 44.
"I had one thing in my mind when I went on my run," he said. "I don't think we had many shots but I managed to connect with it well and scored."
Zaha, who was booked for a lunge on Florent Hadergjonaj, said he was not getting enough protection from referees.
"I feel like I'd have to get my leg broken for anyone to get a card. That's why I lose my head. Why am I getting different treatment from other players? It is every week. I don't know what to say.
"I have tried to speak to the referees. There's nothing I can do any more. It doesn't make you want to go on a run because someone will come through the back of you and it doesn't allow you to express yourself.
"At the same time, I have to let my feet do the talking which I did today."
(Reporting by Neil Robinson; editing by Clare Fallon)
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