Palace produced one of the shocks of the season last weekend to dent Chelsea's title push and boost their chances of remaining in the top flight.
The 1-0 win means Pulis' men are five points clear of this Saturday's opponents Cardiff City, who occupy the last relegation place.
You have to go all the way back to Boxing Day – a 1-0 success at Aston Villa - to find the last time that Palace were victorious on the road in the Premier League.
And Pulis has challenged his players to replicate the committed performance against Chelsea when they head to the Welsh capital this weekend.
"The players have to believe that we can pick up points (away)," he said.
"The group is an exceptional group in respect of togetherness – and that's most probably our strength. They are a very good group of players, even the ones who are not in the team.
"Over 38 games, the harder you work, the luckier you get.
"We're playing against a team who've got very, very good players in a stadium with very passionate fans.
"We've been the underdogs all season and that will continue, irrespective of where we are and what we're doing."
On the win over Chelsea, Pulis – who went to watch Cardiff when he was a kid – added: "It was such a good performance.
"Eight, nine, 10 players were very, very good on the day – and you have to be like that against the top teams.
"It was pleasing. It was three points. But it's gone now. The most important thing is to focus on the next game, which is going to be as difficult.
"Winning games breeds confidence and the way the lads played they can gleam a lot from it, but when we kick off on Saturday that goes out of the window and they have to perform again."
