Jason Puncheon netted a double and Joe Ledley also scored against his former club as the south Londoners moved seven points clear of the drop-zone.
Dann was delighted with another clean sheet for Palace, who pulled off a shock 1-0 win over Chelsea last Saturday, but admits there is still work to be done.
"Yeah obviously it's another big step towards where we want to be and what we want to achieve," said the centre-back.
"Coming here we knew it was going to be a tough game and we turned up today and made sure that we got the right result.
"To get back-to-back wins in this league is a tough ask and to obviously keep two clean sheets, being a defender, that's brilliant but we knew it was going to be tough and there's still a lot of work to do and we need to keep our feet on the ground.
"We've got another big game coming up Saturday and we need to make sure we get the right result there too."
Pulis has added more defensive steel to Palace since he took charge in November, with the club languishing in the drop-zone.
Dann, a January signing from Blackburn, admits the manager deserves plenty of praise for transforming the team's fortunes.
Asked about his contribution, Dann said: "It's obviously massive. He came here before I was here, he obviously brought me to the club.
"We work hard every day in training and he makes sure that everyone knows their jobs and what he expects of them on a Saturday.
"The lads give their all for the manager in every game and I think that type of performance shows what type of manager he is."