Although they have pulled off plenty of impressive results in the Premier League since their promotion from the Championship in 2008, the Potters are yet to earn a point from four encounters with United.
Pulis' side go into Sunday's clash with the Red Devils at the Britannia Stadium having failed to score a single goal in any of those games, while shipping 12 at the other end.
However, they have overcome a disappointing start to the present campaign to take 10 points from their last five league fixtures.
And with new recruits Jermaine Pennant, Jon Walters and Kenwyne Jones having already made notable contributions, Pulis feels the Staffordshire outfit are in good shape to tackle Sir Alex Ferguson's men.
"We think we have improved as a team," Pulis said.
"I think Pennant and (Matthew) Etherington have got real good pace down the sides of the pitch and obviously Kenwyne and Jon Walters have done well up front.
"We've got more in the team to cause people problems, so it is just whether we can perform on the day to our maximum - and hoping that we get a little bit of good luck and good fortune, and that United are maybe just off it a little bit."
United are likely to arrive in the Potteries in positive mood after today's announcement that Wayne Rooney has signed a new five-year contract with the club.
Pulis accepts his players may not see much of the ball, but insists that with it being a home fixture, they will do their utmost to take control of the match.
"We recognise who we are playing - one of the great teams in this country," Pulis said.
"We will have to play to our maximum to get anything out of the game, but we won't be talking about anything else apart from what we can do. That is the way we always approach it at the Britannia.
"We are not playing away, we are playing at home and we have to try and dictate the game.
"We know Manchester United will have a lot of possession of the ball - it is just making sure that when we get it we can affect the game."