An unpopular appointment among many Potters followers when he returned for a second stint as manager in June 2006, Pulis has gone on to oversee arguably the brightest period in the club's history.
Stoke have followed promotion to the top-flight with a maiden FA Cup final appearance last summer and progress to the last 32 of the Europa League this term.
Having masterminded such a startling upturn in Stoke's fortunes, Pulis understandably receives significantly greater support at the Britannia Stadium these days.
Kean, by contrast, has been forced to endure increasing criticism from his own club's fans as the season has progressed, culminating in vitriolic abuse from the stands in the recent home defeat to Bolton that left Blackburn at the foot of the table.
Saturday's stunning 3-2 victory over Manchester United at Old Trafford, which came five days after Kean's men secured a battling point at Liverpool, will surely have eased some of the pressure on the Scot's shoulders.
And Pulis feels Blackburn have a much greater chance of securing survival if they can present a united front in the new year.
"I went to their game against Bolton, and I came out at half-time because I thought it was wrong," said Pulis.
"When you have got a local derby like that, whether they like Steve or dislike him, whether they like the owners or dislike them, the one thing you expect supporters to do for 90 minutes is support their football club.
"If they want to vent their feelings afterwards, fine. But when they are doing it when the game is going on, it is doing their players no good at all and it is doing Steve no good."
Drawing on his own experiences, Pulis added: "I understand the situation - we are in that game and you have to accept that there are people who are going to be for you and those who are going to be against you. You have to be strong and tough enough to accept that.
"I have had it a few times as a manager and it is very difficult for the players on the pitch to give it their best. We are all made differently and some people roll their sleeves up and rise to the challenge.
"Other people wilt, though - it does have an effect. But that is the world we live in and we have to get on with it."
Blackburn could climb out of the bottom three should they win on Monday, while Stoke, who were held to home draws by Aston Villa and Wigan over the festive period, will be hoping to consolidate their position in the top half of the table.