Mathias Doumbe's second-half header from close range was enough to secure the away win for Plymouth.
Rotherham's best chances fell to Richie Barker and Chris Swailes but Moore's side again struggled in front of goal.
It took a smart save from goalkeeper Mike Pollitt to prevent David Norris adding a second for Plymouth, who were marginally the better side.
Plymouth boss Bobby Williamson:
"It was always going to be difficult but it was a good performance and a good
"Rotherham can count themselves unfortunate not to have got a point but we
defended really well and scored a goal from a set-piece, which was pleasing."
Rotherham: Pollitt, Stockdale, Swailes,
McIntosh (Gilchrist 83), Hurst, Sedgwick, Garner (Vernazza 38),
Shaun Barker, Mullin (Proctor 77), Warne, Richard Barker.
Subs Not Used: Montgomery, Scott.
Plymouth: Larrieu, Worrell, Coughlan, Doumbe, Gilbert, Norris,
Makel, Adams (Wotton 90), Dickson (Lasley 84), Crawford, Evans.
Subs Not Used: Hodges, Connolly, Yetton.
Goals: Doumbe 65.
Ref: M Ryan (Lancashire).