Birmingham came into the game with seven points from nine on their return to the Championship, but chased the game for much of the first half.
Leicester boss Marti Cifuentes left out Bilal El Khannouss for the second game in a row, with the Morocco international watching from the stands as speculation grows over his possible exit before Monday's transfer deadline.
The hosts wasted no time in asserting themselves as they prospered from Ethan Laird and Paik Seung-ho failing to pick up the ball deep in the Birmingham half before it fell to Louis Page who set up Fatawu for a left-footed strike to open the scoring.
Birmingham could have sealed a point when Laird fired a shot from close range with just over 10 minutes left on the clock, but he was denied by an impressive last-ditch save from Foxes keeper Jakub Stolarczyk.
Despite Pereira getting on the scoresheet with two minutes left, it was 16-year-old Leicester substitute Monga who stole the show with his sumptuous ball teeing up the full-back to score right in front of goal.
Earlier in the second half, Pereira had been yellow carded rather than shown red for a strong tackle on Furuhashi, with the Japan international limping from the field as he was substituted shortly after.
It was a second defeat in a row in all competitions for Birmingham after they were knocked out of the Carabao Cup in midweek by League One side Port Vale.
For Leicester, however, they have now won four home league games in a row for the first time since April 2024, and move up to third in the Championship, with Blues dropping to seventh.