United substitute Mark Burchill came on to rescue a result for the visitors with a poacher's goal in the 84th minute after pouncing on a mix up between Daggers defender Magnus Okuonghae and keeper Tony Roberts.
The former Celtic player's goal cancelled out a spectacular strike from Dagenham forward Paul Benson early in the second half.
Rotherham bossed the first half and skipper Pablo Mills tried his luck from range in the 10th minute, but saw his thunderous 30-yard effort palmed around the post by Roberts.
The visitors thought they had taken the lead in the 14th minute when Drewe Broughton turned an Alex Rhodes strike into the net only to see his effort ruled out for offside.
United piled on the pressure and found gaps in the Daggers defence, with Danny Harrison losing makeshift full-back Jon Nurse in the 21st minute and firing in a powerful strike which Roberts raced across his goal to block.
The home side were rocking, with United midfielder Reuben Reid out-muscling Solomon Taiwo in the 24th minute before skimming Roberts' post with a thunderous 25-yard strike.
Harrison missed a sitter in the 26th minute when he was put clean through on goal by Broughton only to slide the ball wide from 10 yards with Roberts stranded.
The Daggers soaked up the pressure and finally took the lead out of nothing in the 49th minute when Benson received the ball from Taiwo 25 yards out and fired a vicious shot across Andy Warrington into the corner of the net.
Taiwo came close to making it two just five minutes later when he unleashed a speculative volley from the edge of the United box which Warrington did well to stop.
Rotherham finally grabbed an equaliser against the run of play in 84th minute when Burchill came off the bench to slot past Roberts from six yards.
The home side piled on the pressure in search of a late winner but United held on for a point.