The Millers made 7 changes from Saturdays game and had goalkeeper Viktor Johannson to thank with saves in the penalty shootout.
Will Grigg has a shot well saved by Aidan Stone in the Vale goal after a good cross from Ollie Rathbone early on.
The Millers had appeals for a penalty when Grigg was felled in the Port Vale box after another Rathbone cross, but referee Peter Wright waved away the claims.
Michael Smith put the Millers ahead in the 56th minute after slotting home a Kieran Sadlier cross from close range.
However the Millers couldnt hold on and the game went to penalties after David Amoo brought the visitors level with just 2 minutes left after scoring from a rebound.
With the game going into penalties, the deadlock was broken when goalscorers David Amoo's penalty was saved by Johannson as Amoo placed it down the middle to make the score 4-3 to the Millers. With Joe Mattock scoring the 5th penalty for the Millers.. The Millers progress.