The game opened up scrappily as both sides struggled with the windy conditions, but the first chance fell to new boy Rhodes early on, as he ran through one on one with Rams 'kepper Lewis Price, only to dwell on the ball too long and the chance was gone as Price dove at his feet.
Mark Burchill then fired wide from the edge of the area, with Derby's only major threat coming from the lively Jordan Stewart in the first period.
The Millers made six changes just after the hour mark including trialist Reid, formerly at Plymouth, but the game continued in bitty fashion on a pitch looking a touch bobbly in patches.
Reid impressed down the left and swung a couple of balls into the mixer, but with nobody there to get on the end of them.
John Oster went close for the visitors with a long range effort before a James McEveley free kick whistled over Steve Cann's crossbar.
Millers: Warrington (Cann 62), Tonge (Lynch 62), Mills (Joseph 62), Coughlan (Sharps 45), Green (Todd 62), Yates (Connor 52), Cummins (Harrison 45), Hudson (Haggerty 60), Rhodes (Holmes 54), Taylor (Reid 52), Burchill (Cahill 62).