Not for the first time in his remarkable 10-year career with the Merseyside club, Moyes is again working wonders this season.
Ahead of Saturday's visit to Stoke, Everton are riding high in fourth in the top flight after losing just one of their last 11 league games as they push for a place in next season's Champions League.
Sunday's come-from-behind late show at home to Tottenham, in which Everton scored twice in the dying stages for a 2-1 win, epitomised the team spirit fostered by Moyes.
Given the Scot's managerial qualities, it remains a surprise to Pulis the Scot is still at Goodison Park.
"I know David very well. He is a top manager, has done exceptionally well there. They'll be really pleased they've kept him and that he's still there," said Pulis.
"I'm surprised he is still there, to be honest, because I thought one of the big four might have taken him away after serving a first-class apprenticeship there.
"He's now been there a long time, the players know him, the club know him, he's put his stamp on the place, and they're reaping the rewards from it."
To that extent, given the job Moyes has done, especially on the money he has been able to spend, and Everton's longevity in the top flight, the Toffees represent a role model club for Stoke and Pulis.
That is not to denigrate his own achievements with Stoke or the club itself, but Pulis appreciates City are currently only in their fifth season in the Premier League as he continues to build.
"Traditionally they've been a top, top club over the years, not out of the top flight for many years (since 1954)," added Pulis.
"Everton are a benchmark for us in lots of respects. They're a very good club, with the way they've built and put things together.
"As I've mentioned, they've a great manager, but they've top players, and they've a real chance of pushing for the top four. They'll be top six without a question of a doubt this season.
"We haven't had as much time as Everton in the Premier League to lay the foundations, but we're getting there, and that's the main thing.
"We've had a great year this year. Every year we spend in the Premier League is an achievement. We just want to build the club properly, and over a period of time."
Pulis believes the game will be their "toughest of the year" so far, but it is likely to be the same for Everton.
Stoke are unbeaten in their last 14 league games at home where they have conceded a miserly two goals in seven matches this season.
"It will be as hard a game as we will have at home this year because they do have the tools to cause you problems," said Pulis.
"They've good players on and off the ball, defenders who defend well and players who can also open you up, so it's a massive test for us.
"But the lads have performed brilliantly of late, although they'll be the first to say our defending starts at the front. You defend as a team, as a unit.
"To single out Ryan (Shawcross), Robert (Huth) or Asmir (Begovic)would not be right. It's been done as a team.
"What we have to do is make sure we get some goals at the other end, so we could do with Ryan and Robert scoring a few from some set plays at some point."
Pulis welcomes back midfielder Charlie Adam after completing a one-match ban, but is without right-back Ryan Shotton who serves his own one-game suspension.