Goals from Ashley Barnes and Andre Gray were enough to seperate the two sides, with Palace looking a shadow of their former selves. The result takes the Clarets above them in the Premier League table as a result.
Dyche was visably delighted with his teams performance which all but ensured their survival in the top-flight.
Dyche thanks fans following big win
"It's a big win for many reasons. It's a reward for some hard work on the road and the fans have been amazing again today. They have seen us get close and there have been a couple of games when we were scratching our head as to how we haven't got a victory."
"So to come here with that hanging over you and deliver that performance was terrific. I made a couple of changes today, two enforced and two not, but I thought to a man the lads were fantastic and that win was for those fans."
"When you think we haven't had that win all season and they have just stuck at it and stayed with us week in week out, so that one is undoubtedly for them, as well as us."
Burnley all but secure Premier League survival
The result sees Burnley 14th in the league, eight points clear of the danger zone.
"We have to keep working hard because we are not masters of the universe. But I did feel the win would come and the things I am really pleased about was the mentality of those players. I talked to them in the week about the will and desire to keep going despite what everyone was saying on the outside"
"I thought the focus and organisation was terrific. We grew and grew into the game with a strong tactical performance, some excellent individual performances and two very good goals.
“It’s never easy coming here and they were in a fantastic run of form, so when you put all that in the melting pot it’s a big performance and a fantastic win," concluded Dyche.