The visitors had an early opportunity when Lasse Vibe unleashed a right-footed shot from the centre of the danger area after latching on to Florian Josefzoon's pass, but the effort was blocked.
Birmingham suffered an early injury blow when Maxime Colin went to ground, and he received lengthy treatment before being replaced by David Cotterill, who had not played for the Blues since last month.
Marc Roberts came close to making the breakthrough for the home side when he aimed a header from inside the box, but the ball ended up going wide.
At the other end, Vibe forced a save after charging into the box and letting one fly, but neither side were able to grab the game by the scruff of the neck.
Cotterill's free kick ended up drifting through to Daniel Bentley, who ended up dropping the ball, but the hosts were unable to capitalise as the referee blew for a foul.
Ollie Watkins stepped up to take it and ended up nestling the ball into the bottom left corner, giving Brentford a boost heading into the 15 minutes of the game.
The Blues were unable to respond and they were punished further when Maupay wrapped up the contest with a low strike from the centre of the box.
Brentford move to 15th in the table, while Birmingham sit two points above the relegation zone.