The Frenchman missed a chance to open the scoring after just six minutes, but made amends shortly after when he headed in from close range from a Joshua King cross into the box.
Jordan Rhodes tried to double Blackburn's lead in the 16th minute, but his effort was blocked, allowing Chris Burke to try a volley down the other end, but it went well over.
The visitors did add a second 20 minutes in as Craig Conway curled the ball in from a free kick finding the head of Gestede for his second of the day.
Birmingham's defence let Blackburn in again a couple of minutes later with Todd Kane extending their lead with his shot taking a deflection to ease past Darren Randolph.
Gestede added his third headed goal of the day with the last action of the first half to complete his hat-trick, converting from a corner as the Birmingham players left the pitch to boos from the home fans.