Benitez has had a mixed time of it so far since taking over from the sacked Roberto Di Matteo in November, with a remit to carry out the job until the end of the season.
Under the Spaniard, Chelsea have recorded several high-scoring victories but he was unable to prevent them from crashing out of the Champions League. They were beaten in the final of the Club World Cup and on Wednesday they suffered a 2-0 home defeat in the first leg of their Capital One Cup semi-final against Swansea - a week after losing 1-0 at home to strugglers QPR in the Barclays Premier League.
The appointment of former Liverpool boss Benitez was met at the time by discontent among some Blues fans and, as has been the case at several games since then, he endured a torrent of abuse from a section of the crowd on Wednesday.
Pulis was at the Swansea match ahead of his 10th-placed side's league clash with fourth-placed Chelsea at the Britannia Stadium on Saturday, and the Welshman has emphasised how important it is for managers to be given a decent chance to prove themselves at a club.
Regarding the animosity towards Benitez, Pulis - who has spent 10 years as Stoke boss, aside from a brief stint at Plymouth in 2005-06 - said: "I had it here when I came back after the spell away.
"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."
There has also been talk of another Stoke frontman, Kenwyne Jones, being targeted by Swansea.
Questioned about that, Pulis - who reiterated that he is looking to bring players in during the current window - said: "There is Kenwyne, there has been interest from other clubs in other players.
"There is loads of stuff going on - it is the silly season. So we will let the silly season run and we will decide what is right for the football club and the players.
"We always take everything into consideration at this football club, and if it is right for the players and the football club, we will do business. If not, then we'll get on with things."
One confirmed departure from Stoke is midfielder Michael Tonge, who has joined Leeds on a permanent deal following a loan spell with the npower Championship side.