There was no breaking the deadlock at Oakwell as the two top-half sides failed to find the back of the net.
Despite the draw, both sides remain where they in the league table, prior to the match.
Gianfranco Zola registered his first win as Blues boss as Lukas Jutkiewicz struck 15 minutes from time against the Cottagers.
Fulham had been holding Birmingham to a stalemate but after Ryan Fredricks was sent off, Zola’s side went all out to score, and did so with Jutkiewicz slotting home.
Sam Gallagher’s tenth goal of the season gave Rovers a late victory over QPR.