The reigning champions travel to Selhurst Park on Saturday looking for their first win in four league matches, while Palace, reinvigorated under their new manager, have won three of their last four games.
But Pulis believes Old Trafford counterpart Moyes will eventually lead United out of their current rough patch and is convinced the Scot will get the support and patience he needs to rebuild.
"They've got some outstanding players and I've watched the last three games on tapes and they could have won the games comfortably," he said.
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"Unfortunately - with Dave - they haven't had the breaks, so they've not been able to pick up momentum.
"In time, David will turn it the way he wants it. The people behind the scenes will give David that time.
"Irrespective of what the press and the media will say, he couldn't be at a better club with better people.
"They've been there before, albeit 25-30 years ago, but they were in this position before."
The Welsh boss admits it was a setback to have their last fixture at Everton called off during a good run of form, but praised the Goodison Park outfit for their treatment of the travelling party.
"It's disappointing because were on such a good run," Pulis added. "You want to keep playing when things are going well for you.
"Everton were absolutely fantastic. When the game was called off, they fed the players, they found us a hotel to stay in, they got us training facilities the next day and they paid for everything. They actually paid for everything.
"I just hope the chairman's already paid back what we owe them. As a football club, they deserve a lot of credit for the way they looked after us."