Mansfield led 2-0 when Perry was shown the red card
Stevenage recovered from two goals down to end Mansfield's 15-game unbeaten home league record.
Things looked bleak for Borough after Kyle Perry netted from six yards and then doubled the home side's lead with a left-foot shot from inside the box.
But the game turned on Perry being sent off for a boot to Lee Boylan's face.
Chris Beardsley headed in a cross from Charlie Griffin to pull one back, and Yemi Odubade equalised from 12 yards before Griffin poked in the winner.
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