Moyes has endured a tough start to life in charge at Old Trafford with United currently 11 points adrift of the top four.
Palace, who have won their last three home matches, host United on Saturday knowing a victory could move them to within three places of the defending champions.
But Pulis insists Moyes was the right man to succeed Sir Alex Ferguson and will, in time, get the Red Devils back on track.
"David has had a tough start but they have some fantastic players," said Pulis.
"I've watched their last three games on tape, and they could have won them all comfortably. They just haven't had the breaks, that momentum to take them forward.
"Last year under Sir Alex they didn't play as well as the year before, but they got the breaks
"This year they've not been able to pick up any momentum. But they have wonderful players and are a wonderful football club and we will be proud to host them.
"When I was manager at Gillingham Moyesy was at Preston and we locked horns there. He'll know what we're about and he'll pick a team to win the game.
"David will turn it the way he wants it. He will be given the time to turn the club around like Sir Alex did when he first got the job. It's a proper football club.
"Irrespective of what the media say, he will be afforded time. They've been in this position before. But David is a top manager and a top bloke. If they stick with him, and I'm sure they will, he will be successful.
"I just hope their luck doesn't change on Saturday."
While a top-10 spot might be within Palace's reach this weekend, they remain very much in the relegation scrap with just eight points separating 11 teams at the bottom.
And Pulis remains in no doubt about the Eagles' prime target this season.
"How many points do we need? One more than the team who finish 18th," he added.
"You have to go out and try to win every game, I don't think you can look any further than the next game in this league.
"If you win games you have to keep your feet on the ground and if you lose games you dust yourselves down, get up and get ready for the next one. That's the way it will be from now until the end of the season.
"From 10th downwards it is really competitive. You have to keep your heads and hope and pray things will drop for you."
Pulis will hand a late fitness test to winger Jerome Thomas, who is struggling with a back strain.