A spell of Spireites pressure then culminated with Sam Morsy sending a low effort wide from the edge of the 18-yard box.
After the break, Madden fired Scunthorpe in front after doing well to find space in the six yard box.
The eventful start to the half continued as Chesterfield were awarded a penalty following a Miguel Llera handball, but Doyle wasted the opportunity by smashing the spot kick onto the bar.
Doyle made up for the miss, however, by firing home from 12 yards minutes later to level up the scores.
The striker's rollercoaster of a game then saw him dink the ball in over Robert Olejnik and he completed his hat-trick by slotting home Chesterfield's second penalty of the game.
Morsy eventually sealed all three points for the hosts after sweeping the ball past Olejnik and into the far corner just before the full-time whistle.