Pulis, who worked wonders to keep Crystal Palace in the Premier League last season, has made a promising start to his bid to revive West Brom's fortunes and masterminded a 7-0 thrashing of Conference side Gateshead in the last round.
The last time West Brom made the short trip to St Andrew's was under the guidance of Roy Hodgson in 2011, when the visitors prevailed 3-1 in a top-flight match.
That extended West Brom's unbeaten run against their Midlands counterparts to three matches, with Birmingham having last tasted victory in 2006.
Pulis has been keen to bring in new players during the January transfer window, but has so far been frustrated in his efforts to recruit the likes of winger Callum McManaman from Wigan Athletic and Manchester United midfielder Darren Fletcher.
They have one new injury concern ahead of the game against Gary Rowett's Championship side.
Midfielder James Morrison, who has made 21 appearances for the club so far this season, has a knock and is a doubt.
Defender Jonas Olsson is still recovering from Achilles surgery, while midfielder Youssouf Mulumbu is on African Cup of Nations duty with Democratic Republic of Congo.
Birmingham go into Saturday's contest on a four-match unbeaten run, which features three wins, including the 3-2 victory at Blyth Spartans in round three.
Since Rowett took over as manager for the league game at Wolves on November 1, Birmingham have won eight of 13 matches.
This has seen them climb from 23rd in the table to 11th, just nine points off the play-off places.
"All I will do all the time is keep trying to win games of football and keep trying to work very hard in the week with the players and see if we can keep moving forwards in terms of developing the team, developing the philosophy, making the players better if we can, and constantly trying to improve that squad," Rowett told Birmingham's official website.
One player who has excelled under Rowett and has the chance to further enhance his growing reputation this weekend is winger Demarai Gray.
The 18-year-old, who has scored four goals in 22 appearances this season, was this week named the Football League's Young Player of the Month for December.
