Millers 2 Dagenham & Redbridge 1
Dagenham boss John Still said he thought the referee had got it "horribly wrong" and Rotherham manager Mark Robins admitted he had some heart-stopping moments in the second half after his team had totally dominated the first period.
Rotherham had the advantage of a sixth-minute lead, the goal coming from the penalty spot.
Tom Cahill burst into the penalty area only to be bundled over by Scott Griffiths. Mark Hudson sent goalkeeper Tony Roberts the wrong way to give the home side the early advantage.
But five minutes later Dagenham came very close to an equaliser. David Rainford got his head to Glen Southam's free-kick but directed his effort just over the bar.
Rotherham continued to dominate the pace and had several chances with Dale Tonge firing just over the bar and Danny Harrison pulling a shot just wide.
But in the 41st minute Harrison made no mistake when he doubled Rotherham's lead. Marc Joseph's cross was headed clear by Dagenham but only to Harrison on the edge of the area and he picked his spot with a delightful volley in to the top corner that gave Roberts absolutely no chance.
Only a brilliant save by Roberts just 25 seconds into the second period denied Cahill Rotherham's third but the half-time break certainly revitalised the visitors.
Griffiths and Ben Strevens both went close before Strevens pulled one back for the visitors after 52 minutes, bundling the ball into the net off his body from Southam's corner kick.
And two minutes later Dagenham came very close to a second when Andy Warrington was at full stretch to keep out a shot from Jon Nurse.
But hard as Dagenham tried they could not find a way through Rotherham's rearguard until, deep into stoppage time, when they did get the ball in the net, the effort was ruled out for handball.