Argyle took the lead with a superb attacking move down right, finished crisply by experienced midfielder Ralls from eight yards.
Bali Mumba's defence-stretching pass sent Owen Dale away down the wing and his cut-back cross was deftly first-timed home by Ralls.
United's Tom Holmes headed just over the bar from a 15th-minute corner taken by Dan Gore.
Argyle skipper Joe Edwards made a superb 29th-minute block to deny Joe Powell as he powered a volley goalwards from just inside the box.
Argyle had penalty shouts for a handball waved away by referee David Rock in the 32nd minute.
Jordan Hugill flashed a close-range header just over in the 50th minute, first to a pacy pinpoint cross from the left by Powell.
Hugill also had a shot deflected just wide as Rotherham went in search of a leveller.
Powell's goal-bound 70th-minute drive was saved low at his near post by Conor Hazard.
Mitchell made a brilliant 82nd-minute off-the-line clearance as Holmes headed over Hazard.
