Dagenham twice led through Paul Benson and Danny Green only to see Millers striker Ryan Taylor swiftly level twice but Nurse’s scruffy strike with 20 minutes left proved enough to see off Ronnie Moore’s men.
The Daggers took the lead in the 38th minute through the prolific Benson. Benson showed his predatory instincts to kill the ball with one touch before curling a shot into the bottom corner.
The Essex side were ahead for just 58 seconds though, as Taylor replied in the 39th minute.
A quick throw on the left was hooked in by Kevin Ellison and Taylor arched his back to head past Roberts at his near post.
Dagenham regained the lead in the 56th minute.
Green was 25 yards from goal when he took a touch before thumping a low drive beyond Warrington.
The Millers levelled through Taylor again in the 61st minute. Nicky Law picked out Taylor, who took his time before dispatching a left-footed drive past Roberts and into the right corner.
Dagenham went in front for a third time in the 70th minute. Green’s corner caused chaos in the penalty area and when Nurse mishit a shot Ellison could only divert the ball home off his thigh.
DAG & RED: Roberts, Ogogo, Arber, Doe, McCrory, Green, Vincelot, Gain, Nurse (Montgomery 72), Scott (Walsh 83), Benson.
ROTHERHAM: Warrington, Lynch, Sharps, Fenton, Gunning, Law, Harrison, Mills (Marshall 77), Ellison (Bell-Baggie 86), Taylor, Le Fondre.
Referee: James Linington (Isle of Wight).