There was resistance to the appointment of Benitez as interim boss from the outset and that has only grown after a series of disappointing results culminating in the home defeat to Swansea in midweek.
But Pulis, who has spent 10 years as Stoke boss, aside from a brief stint at Plymouth, believes the Spaniard can turn things around - if he is given the chance.
"I had it here when I came back after the spell away," said Pulis.
"You have to grind it out and get through it. You have to get results and that is what Rafa will have to do.
"If he gets results and he gets lucky, then he has a fantastic football club to build.
"He has proved before at football clubs that he can manage at the highest level.
"Given the chance, who is to say he couldn't do it at Chelsea?
"But he needs the opportunity, and that does not mean weeks or months - you have got to give people time."
Stoke host Chelsea at the Britannia Stadium on Saturday.