Niall Davie had given the Millers the lead midway through the first half with a super strike into the top corner from the edge of the box after fine approach play from Nat Watson and Tyler Blake. It was no more than Carlton deserved after early chances for Aaron Opoku and Blake.
Stratford responded in the second half. Within a minute of the restart Daniel Vann headed home unmarked to bring the visitors level.
The key moment of the game followed shortly afterwards when Liam O'Brien in the Bards goal saved a Nat Watson penalty. Within minutes Stratford were 2-1 ahead after Jaanai Gordon's shot took a heavy deflection off Tyler Johal to wrongfoot Jack Steggles.
Stratford secured the win with nine minutes remaining when Will Grocott fired home a free kick from just outside the area to inflict Carlton's first defeat of the season.
The Millers return to action on Tuesday night when they entertain Sutton Coldfield Town at Stoke Lane.
A full report on today's game will be on site tomorrow.